Broady thrashed Japan's Kaichi Uchida 6-1 6-1 and will now meet Junior Wimbledon champion Filip Peliwo, of Canada, in Sunday's final.
It will be Broady's second Grand Slam singles final - he was runner-up at Wimbledon in 2011.
On Sunday the 18-year-old will be bidding to become the third Briton in the last decade to win the boys' title at Flushing Meadows after current world number four Andy Murray in 2004 and Oli Golding last year. Heather Watson also won the girls' title here in 2009.
Reflecting on his win, Broady said on his Twitter feed: "(I've) finally got my chance at another slam final after just over a year.
"Feeling a lot less nervous and looking forwards to the battle."
Broady has beaten Peliwo in both their previous meetings, including at the Canadian Open Junior Championships last week.