Donald Trump has been declared the winner of the New York primary, a crucial state in the hotly contested Republican presidential nomination race.

The billionaire property tycoon was long predicted to claim the state, with CNN declaring the winner the moment the polling booths closed at 9pm local time (11am AEST).

"We're going to use our great businesspeople to negotiate unbelievable deals," Trump told a crowd during his victory speech.

"We're going to keep the jobs here. You're going to be very proud of this country very soon."

"Nobody is going to mess with us."

His main rival in the race, Ted Cruz, is coming in at a very distant third place, with Ohio Governor John Kasich in second.

Cruz, a senator from Texas, struggled in the state after slamming Trump several months ago for his "New York values".

"Senator Cruz is just about mathematically eliminated," Trump told his rally.

"We've won close to 300 delegates more than Senator Cruz. We're really, really rocking."

Curiously, the only part of the state Trump did not win was Manhattan, where he lives.

Cruz's concession speech has been widely mocked on social media for the awkward phrasing of one of his analogies.

"You may have been knocked down, but America has always been best when she's lying down with her back on the mat and the crowd's given the final count," he said in Philadelphia.

"It is time for us as a nation to get up, to shake it off, and be who we were destined to be."

Meanwhile, Hillary Clinton has been declared the winner of the Democratic primary over Bernie Sanders.

"In this campaign we've won in every part of the country. From the north to the south, to the east to the west, but this one's personal," Clinton told a victory rally in New York City.

"There's no place like home."

Clinton represented the state in the Senate from 2001 to 2009.

Sanders also had a claim as the local candidate, growing up in Brooklyn before moving to Vermont in the 1960s.

Clinton won big in New York City, especially in Manhattan and the Bronx.

Hillary Clinton signs autographs after voting in Chappaqua, New York. (AAP)