The young Frenchman has completed a five-and-a-half-year transfer deal.
Financial details were not disclosed by Leeds but British media reported it was for a fee rising to €40 million.
Rutter scored 11 goals in 64 appearances for Hoffenheim after joining from Stade Rennais in 2021.
"Georginio is a good character and has enormous talent.
"No coach in the world likes to lose a player like him. But of course, I wish him all the best for his future," Hoffenheim head coach Andre Breitenreiter said.
Leeds said that Rutter could make his debut against Brentford on January 22nd.