Mr Trump's shock victory in Wisconsin put him over the 270 out of 538 electoral college votes needed to win the White House, after a gruelling and rancorous campaign.
The US president-elect took to the stage with his family at his victory rally in a New York hotel ballroom and said: "I just received a call from Secretary Clinton. She congratulated us on our victory.
Media captionCheers at Trump HQ, tears at Clinton HQ
"Hillary has worked very long and very hard over a long period of time, and we owe her a major debt of gratitude for her service to our country."
He added: "It is time for us to come together as one united people."
The real estate tycoon, former reality TV star and political newcomer, who was universally ridiculed when he declared his candidacy in June last year, said his victory had been "tough".
Mr Trump has so far won 28 US states, smashing into Mrs Clinton's vaunted electoral firewall in Pennsylvania and Wisconsin, states that have not supported a Republican presidential candidate since 1988 and 1984 respectively.
He also prevailed in Iowa, which has not elected a Republican since 2004.
Mr Trump held on to solidly Republican territory, including in Georgia, Arizona and Utah, where the Clinton campaign had invested resources in the hope of flipping the states.
Image copyrightGETTY IMAGESImage captionA group of Clinton supporters react as election results trickle in
Mr Trump will take office in January with Congress fully under Republican control as Democrats were unable to wrest control of the Senate in Tuesday's general election.
Mrs Clinton, 69, has only notched up victories in 18 US states and the District of Columbia.
New Hampshire and Michigan - which had also been expected to fall in the Clinton column - remained too close to call as of Wednesday morning.
The Democratic candidate, who dreamed of becoming the first female US president, did not show up for what was meant to be her victory rally across town in Manhattan.
The mood was dark at her election night party in the Javits Center, as supporters wept and left early.
At Trump headquarters earlier, his fans cheered and chanted about the Democratic nominee: "Lock her up!"
Media captionUS election: Relive the wild ride in 170 seconds
In other developments:
Russian President Vladimir Putin congratulated Mr Trump, saying he was hopeful of "bringing US-Russia relations out of their critical condition"
As the result became clear, crowds outside the White House broke out into spontaneous protests whileTrump supporters cheered
Massachusetts, Nevada and California voted to legalise recreational marijuana, which could lead to the creation of the largest market for marijuana products in the US
Nationwide exit polls underscored America's stark divide.
Male voters were much more likely to back Mr Trump, while women backed Mrs Clinton by a double-digit margin.
Nearly nine in 10 black voters and two-thirds of Latinos voted for the Democrat, but more than half of white voters backed the Republican.
Mr Trump, a populist billionaire, provoked controversy on the campaign trail for comments about women, Muslims and a plan to build a wall along the US-Mexican border.
He fired up white, working-class American voters who were angry at the Washington establishment and felt left behind by globalisation.
On the eve of the vote, Mrs Clinton was ahead by four points in a BBC aggregate of opinion polls, but it was well within the margin of error.
She saw her campaign dogged by FBI investigations into whether she abused state secrets by operating a private email server during her time as US secretary of state.
Last Sunday, the law enforcement bureau cleared her once again of any criminality.
Mr Trump and Mrs Clinton were vying to succeed Democratic President Barack Obama.
After two four-year terms in the White House, he was barred by the US constitution from running for re-election.
Stewards and riot police intervened when fans came together in the stadium
Crowd trouble marred West Ham's EFL Cup fourth-round home win over Chelsea, with police making seven arrests.
Plastic bottles, seats and coins were thrown during the Hammers' 2-1 victoryat London Stadium as hundreds of supporters clashed and riot police entered the concourse.
It is the latest outbreak of disorder at West Ham's new ground this season.
West Ham boss Slaven Bilic called the behaviour "unacceptable", adding: "We are totally against it as a club."
The Premier League club says it will ban any fans involved for life and is confident it can identify those responsible via its high-definition CCTV system and through fans' ticket purchasing history.
The Football Association and EFL are also investigating. A league spokesman called the incidents "distasteful and unwelcome".
Until Wednesday's match, the Metropolitan Police have not deployed officers inside the stadium because the radio system emergency services use to communicate will not be operational until 2017.
This season, the Hammers' first at the former Olympic Stadium following their move from Upton Park, 23 fans have been banned from the ground.
Four people were arrested following disorder at the Premier League match against Middlesbrough on 1 October, while there were clashes in the stands during the defeat by Watford in September.
The Metropolitan Police, who made seven arrests for alleged public order offences, described Wednesday's incidents as "unacceptable" and said 30 people were prevented from attending the match.
It said part of its investigation will include "a leaflet handed out before the match containing homophobic contents".
Images on social media before the game appeared to show a song sheet being distributed with homophobic lyrics aimed at Chelsea defender John Terry and striker Diego Costa.
West Ham told BBC Sport it was "investigating the alleged distribution of these flyers" and would "take the strongest possible action against those responsible".
Bilic added: "For those kind of things to happen, especially in England, is unacceptable."
Chelsea manager Antonio Conte said: "I don't really like to see these situations."
One fan at the game told BBC Radio 5 live it "was an absolute nightmare", adding: "If they don't close that stadium someone will get killed there."
West Ham said in a statement they "unreservedly condemn" fans' behaviour and will work to identify those supporters involved, while Chelsea said they were "extremely disappointed to see disturbances".
Police commander BJ Harrington said: "There were a minority of people who attended the match that were clearly intent on being involved in confrontation and violence.
"Despite extensive work with both clubs and a large and robust policing operation, there were unacceptable incidents inside and outside the stadium, before, during and after the game."
Chelsea season ticket holders Paul Streeter and his eight-year-old daughter, Victoria, were sitting in the disabled section and got caught up in the violence.
"My daughter was hit with seven coins all over her body", said Mr Streeter. "We were watching the game in the front row near to the home fans - suddenly there's a whole load of coins coming over. Other kids were hit, it was not just my daughter.
"Victoria has been going to football since she was two, she's never experienced violence like this before or the aggression we have had to suffer. We want to take this matter further. It is disgusting.
"Stewards and police were not reacting. They should have dragged the crowd back and dealt with them."
'An agenda against West Ham'
West Ham fan and blogger Sean Whetstone told BBC Radio 5 live that coins were thrown by some Chelsea fans and some West Ham fans then retaliated.
He said: "Football has trouble, but it is not reported elsewhere. There is trouble at Stamford Bridge every season when West Ham play Chelsea. It feels like there is an agenda against West Ham.
"There is a limited amount of police inside the stadium. It is the stewards' job to sort that out inside the stadium. They have learned a lot already but there is much to do.
"It is a new stadium, an iconic stadium and I believe that a small amount of away fans come to prove a point. Are some West ham fans unhappy? Do they feel unsafe? Yes they do.
"West Ham are doing enough. They have the best CCTV available and they will look at all of the footage and anyone who threw anything will be banned for life. There is zero tolerance."
Chelsea fans Paul Streeter and his daughter, Victoria, with the coins they say were thrown during the disorder
'Atmosphere turned toxic'
BBC's Richard Conway at London Stadium:
With West Ham cruising towards the quarter-finals of the EFL Cup their fans were taking great delight in taunting Chelsea's 5,000-strong support.
Then tension and vitriolic chanting turned into violence. Fans told me after the game how they and their children were pelted with coins.
The atmosphere turned toxic, with attention now focused not on the pitch but on events in the stand.
A Chelsea fan broke through a line of stewards into the area dividing supporters, balancing on the tops of seats covered in claret tarpaulin. He goaded his rivals before retreating.
Then the two sets of fans surged towards one another on the stadium concourse, which sits at the top of the lower section of the ground. It took a number of stewards, eventually backed up by riot police, to quell the standoff.
The final whistle came soon after and fans eventually left the stadium. But the damage by then had been done.
I started watching football as a kid in the mid-1980s, when fan violence was rife within the game. The end of this match made it feel like I had momentarily stepped back in time.
A fan gets past a cordon of stewards to approach West Ham fans
'Sad scenes'
BBC Radio 5 live presenter Jonathan Overend, commentating on the game, said: "This has been brewing all night.
"It's been hard to watch the match because of the flash points developing. The stewards have got a tough job here. Fans are trying to burst at each other.
"They've been hurling missiles at each other. It looks like plastic bottles and I've seen what looks like three or four plastic seats being thrown."
Seats, coins and plastic bottles were thrown by fans
Image copyrightKATSUHIKO TOKUNAGAImage captionThe deal with Saudi Arabia would be a lifeline for BAE's Eurofighter Typhoon programme
BAE Systems has disclosed it is in talks over a multi-billion-pound arms contract with Saudi Arabia.
The announcement by the defence, aerospace and electronics giant will stoke controversy over weapons sales to the Arab kingdom.
However, it will hold out a lifeline to aircraft factories in the North West.
The UK has been one of the biggest suppliers of defence equipment to Saudi Arabia for more than 40 years, including the 1980s al-Yamamah deal.
That deal - worth more than £40bn, according to former BAE chief executive Mike Turner - was credited with saving the company from a near financial crisis.
But the supply of arms has come under renewed scrutiny after Saudi Arabia's recent attacks on Yemen.
The BBC's Newsnight recently revealed that an influential select committee had compiled a draft report calling for a ban on all exports. A final report from the committee has yet to be released.
Foreign Secretary Boris Johnson has told the Commons that the government had accepted Saudi assurances that British weapons were being used in accordance with international law.
For BAE, a new Saudi deal would be an important fillip. Talks have been underway for more than two years over a five-year deal centred on the sale of 48 Eurofighter Typhoon combat aircraft.
Typhoon production in the UK - which takes places at factories in Warton in Lancashire - is slowly winding down because of a lack of export orders.
At current rates, production would cease in about five years' time. The sale of another 48 aircraft would significantly extend the factories' lives.
BAE told the Stock Exchange on Thursday: "Discussions between BAE Systems, the UK government and the Saudi Arabian government are progressing to define the scope and terms of the next five-year Saudi-British Defence Co-operation Programme."