With the majority of votes counted, Mr Trump looks set to extend his lead over rivals Ted Cruz and John Kasich.
Meanwhile Democratic hopeful Mrs Clinton, a former senator for New York, is on course for a resounding victory over Brooklyn-born Bernie Sanders.
Wins will put Mrs Clinton and Mr Trump closer to securing their nominations.
With almost 95% of the results in, Mr Trump is leading with just over 60% of the vote while Mrs Clinton has just under 58%.
New York primary results