The 18-year-old saw off Japanese eighth seed Kaichi Uchida to make it through to his second Grand Slam final in two years.
The 13th seed will now face Canadian Filip Peliwo in Sunday's final at Flushing Meadows.
"Finally got my chance at another slam final after just over a year," he tweeted. "Feeling a lot less nervous and looking forwards to the battle."
Broady narrowly lost the boys' singles final at Wimbledon last year.