The 19-year-old forward has joined United from Arsenal for an undisclosed fee, having impressed for the Gunners age group sides and at international level.
Greenwood has been capped for England at youth level and scored 12 goals in 14 games for the Under-17s, with whom he also played at the 2019 European Championships.
The north-easterner caught the eye at under-18 level at Arsenal last term and also featured five times for the Gunners in the Premier League 2 at under-23 level.
Greenwood will initially link up with the under-23s and becomes the latest young player to join Leeds following the arrivals of Charlie Allen, Cody Drameh, Joe Gelhardt and Dani van den Heuvel.
On his move, Greenwood, who has signed a three-year deal until the summer of 2023, said: "I cannot wait to get started. It is such a big club and it is exciting times for the club.
"For me, it seems like it has such a good pathway for young players to come through. It is such an exciting manager and the fans are special.
"I look up to players like Kalvin Phillips all the time - he has broken into the England squad and it is a very proud moment for him and I am sure he will be over the moon with that and something I would love to do in the future.
"Arsenal is a great club and I have met some great people along the way, but for me in my career, it is perfect time to come to Leeds and kick on now.
"My target is to hopefully try and make a breakthrough and hopefully make a name for myself among the Leeds fans and kick on."
The move sees Greenwood - who started his youth career with Sunderland before joining Arsenal in 2018 - head back up north and that was another positive factor for the striker.
He added: "I started at Sunderland and got the move to Arsenal. Now I have come here, I feel like I relate to these people. Obviously, Sunderland is a working-class area similar to Leeds and I think I will fit in at this kind of environment perfectly."
On what Leeds fans can expect, he continued: "I am a striker who is both footed and like to make runs in behind and like to run at defenders and find half a yard and get my shots off."