The 18-year-old has been a regular at Elland Road this season and was named as the club’s Young Player of the Year and the Championship's Apprentice of the Year after some impressive performances.
And the York-born player has committed his future to the Yorkshire club until the summer of 2017 as he looks to get more first-team experience.
"I’m over the moon, all the hard work this season has paid off I think," Cook told LeedsUnited.com.
"I’m delighted to sign with Leeds United, I’ve really enjoyed this last season. I’m enjoying my football and enjoying being here. I’ve got no regrets.
"I’ve been getting a lot of people asking me about my future and hopefully they’ll be happy.
"I’m going to go away, rest and prepare for the new season."
Cook has been a Young Lions regular over the last three years, earning caps at U16, U17 and U18 level.
He was part of John Peacock’s U17s team who won the European Championship title just over a year ago, before progressing into the U18s squad this season and finishing the campaign with the U19s in March.