The 18-year-old has signed a three-year contract at Elland Road, running until the summer of 2023.
The striker started his youth career with Sunderland, before joining the Gunners in 2018 after impressing on Wearside.
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.
At Arsenal last season after catching the eye for the Under-18s, he made the step up to Under-23s football, featuring five times for the Gunners in the Premier League 2.
Greenwood will initially link up with the Under-23s and becomes the latest young player to join the club during the summer transfer window, following the arrivals of Charlie Allen, Cody Drameh, Joe Gelhardt and Dani van den Heuvel.