The 18-year-old midfielder, who recently claimed the 2014/15 Young Player of the Year award, capped a fine breakthrough season by extending his Elland Road stay until at least summer 2017.
Cook, a graduate of United’s famed Academy system, made 38 appearances in all competitions last season and received international recognition for England Under-19s along the way.
The midfielder had a year remaining on his previous contract, but has now put pen to paper on a fresh two-year deal as the club prepares for the new campaign.
Speaking on the official Leeds United website, he said: "I’m over the moon, all the hard work this season has paid off I think," he said.
"I’m delighted to sign with Leeds United, I’ve really enjoyed this last season."
Asked if he needed much persuading, Cook replied: "Not at all, I’m enjoying my football and enjoying being here. I’ve got no regrets.
"There was a bit of speculation around it all, but as soon as I was told I was going to be signed, I did it.
"Hopefully a few more signings will be brought in to strengthen the team and next season could be great.
"I’ve been getting a lot of people asking me about my future and hopefully they’ll be happy."
Cook now hopes that the club will keep hold of the other bright prospects and fellow Academy graduates who have progressed with him through the ranks to make the first team.
"I guess that’s the plan," he said. "If we can do that, then it’ll solidify next season and make the fans happy. Hopefully we can push on.
"I’ve been injured but I’m feeling a lot better now so I can really think about pre-season and try and kick on.
"I’m going to go away, rest and prepare for the new season."
Reflecting on the past 12 months, Cook added: "It’s been a whirlwind for me, I would never have dreamt it. I never thought I would have played as many games as I did.
"I’ve really enjoyed it. The Bournemouth game was one of my highlights, as was that little run we went on where we won six or seven games."