The three-and-a-half-year contract extension will keep the 18-year-old at Elland Road until the summer of 2017.
Mowatt told Leeds' official website: "I'm really pleased to have signed. I've been at the club since I was six and this is where I want to play my football.
"This season has gone really, really well so far, and I just want to keep working hard, keep improving, and play my part in helping Leeds United get where we want to be."
United's managing director David Haigh said: "We're delighted we've agreed a new contract with Alex. He has been at the club most of his life, and his development and progress is a testament to the work of the club's Academy.
"The development of our own players is something we see as vitally important, and we look forward to Alex being a part of our future here."
Manager Brian McDermott said: "Everyone at Leeds United is delighted that he has committed his long-term future to us.
"Playing regular football as an 18-year-old in the Championship tells you exactly what we think of him."