The France u-21 international has signed a five-and-a-half-year contract at Elland Road.
Rutter is Leeds' second winter signing after Maximilian Wober joined from RB Salzburg earlier in the window.
Rutter had been at Hoffenheim since February 2021 after joining from Rennes, and made 64 appearances for the club, scoring 11 goals and providing 11 assists.
He told Sky Sports News: "There's a lot of emotion today. It's an important day. I'm very happy to be here and I'm very excited to start.
"I run and I bring a lot of energy to the pitch. I like dribbling and playing beautifully, scoring goals and getting assists. I hope [I can get the goals that take Leeds up the table]."
"We regret the premature departure of this highly talented player, who is not only a great guy but also has the ability to provide spectacular moments on the pitch," said Hoffenheim director of football Alexander Rosen.
"In light of the third-highest transfer fee in the club's history, as well as the clearly communicated desire to move, it would not have made sense to block a young player like Georgi from the path he is pursuing. I'm sure I'm not the only one who will miss him.''
Leeds are 15th on the Premier League table, two points above the relegation zone.
Rutter could make his debut for the club against Brentford next weekend.
