Midfielder Mowatt, the club's Under-18s captain, has signed a two-year deal and is the fifth of this year's scholars to sign professional terms at Elland Road.
"I'm delighted," Mowatt told the club's official website. "I've worked hard this year and hope this is the first step.
"Everyone has done really well in the Under-18s this season and I hope we can go on and win the league now."
Mowatt is hoping to follow former team-mate Sam Byram into the first-team squad.
He added: "I played with Sam a lot last season and he's a great example.
"He's played nearly every game and has been quality. He got the opportunity and took it. He shows there's a chance."
Strikers Luke Parkin and Lewis Walters, plus goalkeeper Eric Grimes, signed their first contracts earlier in the week.