The 18-year-old Academy graduate, whose existing deal was due to expire in the summer of 2016, will now be contracted at the club until June 2017.
Cook featured 38 times in all competitions in a stunning breakthrough season after making his debut on the opening day of the campaign at Millwall.
Cook has since gone on to represent England at Under-19s level and was acknowledged at the recent Football League Awards, claiming the LFE Apprentice of the Year award, before being named as United’s Young Player of the Year .
Chairman Massimo Cellino said: “Lewis Cook deserves his new contract, he was one of the most exciting players last season.
“I knew we had a wonderful talent when I first saw him in the summer.
“At first, I thought he was much older than he was. He plays like he has lots of experience.
“My hope is for him to stay at Leeds for a long time and continue growing with Mowatt, Byram, Taylor and the others. We don’t want to sell.
“My plan for this club is to grow, not to sell our best young players.
“I have a lot of trust in the young players here. It is a special place for them and it has been for many years.
“Young players at other clubs say they love their club, but they don’t really mean it.
“Here at Leeds, I can tell they mean it. The club is really in their hearts.”