United did not disclose the amount they will pay the German club for the 20-year-old, but it has been reported it could rise to £35million depending on certain clauses being met.
Rutter, who has scored 11 goals and added 11 assists in 64 appearances since joining Hoffenheim in February 2021, has signed a five-and-a-half year deal at Elland Road, Leeds' second signing of the January window after Max Wober.
Leeds want Rutter to boost their attacking options as he can play either in a central role or in wider positions cutting in from the flank.
Crysencio Summerville and Luis Sinisterra are in the treatment room while fellow forward Patrick Bamford has a chequered injury record.
Jesse Marsch was certainly in need of a boost, having been forced to deny his side were at risk of relegation after Friday night's 2-1 defeat to Aston Villa made it seven games without a win in all competitions.
Rutter will not be eligible for Wednesday's FA Cup replay against Cardiff but should come into contention for next weekend's Premier League match against Brentford.
Rutter first came through with Rennes, and scored his first professional goal in a Champions League match against Sevilla aged 18.
Hoffenheim snapped him up only a couple of months later and he made a name for himself in the Bundesliga as an exciting young talent.
The striker has become Leeds' second signing of the month following the arrival of Austrian defender Wober from RB Salzburg.