Mrs Clinton, after beating Bernie Sanders, said her victory for the Democratic nomination was in sight.
BBC
Mr Trump looked set to take nearly all the 95 Republican delegates at stake.
He said his nearest rival Ted Cruz was “just about mathematically eliminated”.
With more than 98% of the results in, Mr Trump is leading with just over 60% of the vote while Mrs Clinton has just under 58%.
US networks projected that Mr Trump had won in his home state barely seconds after the polls closed at 21:00 EDT (01:00 GMT).
Speaking at Trump Tower in Manhattan, he said: “I have to say to the people that know me the best – the people of New York – when they give us this kind of a vote it’s just incredible.”
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Donald Trump needed a commanding victory, and he got it. Although the results in the state’s 29 congressional districts – which allocate three convention delegates apiece – have yet to be finalised, it appears likely that Mr Trump will claim the lion’s share of the 95 delegates at play.
Perhaps even more importantly, however, is the new, restrained Donald Trump on the campaign trail in the past few days. Gone are the incendiary tweets bashing his opponents (and their spouses).
Instead on Tuesday night the candidate gave a short speech hammering home his economic message, emphasising his delegate and vote lead, and laying the groundwork to argue that he should be the party’s nominee even if he doesn’t win the 1,237 delegates necessary to claim the nomination outright.
Mr Trump recently brought in several experienced political hands to manage his campaign after a turbulent few weeks. If this new demeanour is part of the change they have inspired, Mr Trump could prove to be a more formidable opponent not just at the ballot box in upcoming primaries but in the contest to win over those in the party still deeply suspicious of his candidacy.
“Tomorrow, we go back to work,” Mr Trump said during his victory speech. It was a very un-Trump-like line – and something that should have his opponents very concerned.
He said he was going to get more delegates than “anyone projected even in their wildest imaginations”.
Third-placed John Kasich picked up three delegates in New York.
Mrs Clinton told supporters her campaign for the nomination was “in the home stretch and victory is in sight”.
“New Yorkers, you’ve always had my back and I’ve always tried to have yours,” she said. “Today together we did it again and I am deeply, deeply grateful.”
It had been a fierce campaign in the state, with Mrs Clinton – a former New York senator – and Mr Sanders – born in Brooklyn – using their local ties to attract voters.
The Democratic campaign has turned increasingly negative, with Mrs Clinton and Mr Sanders trading barbs about their qualifications.
But following the latest result in the race for the Democratic nomination, Mrs Clinton said there was “much more that unites us than divides us”.
The voting in New York was marred by widespread complaints of irregularities, including more than 125,000 people missing from New York City voter rolls. The city’s chief auditing officer, Scott Stringer, ordered a review of the city’s Board of Elections (BOE) over what he called “chaotic and inefficient” organisation.
Bernie Sanders, who has vowed to fight on in the nomination process, spent Tuesday in Pennsylvania before heading home to Vermont for a day off the campaign trail.
Republican hopeful Mr Cruz, whose criticism of “New York values” attracted scorn in the state, had also moved on to Pennsylvania. He dismissed the New York primary result as nothing more than “a politician winning his home state”, according to the Associated Press news agency.
Pennsylvania is the most important of five states holding both Republican and Democratic primaries on 26 April, and then candidates will look to score successes in Indiana on 3 May.
