Hoffenheim coach Rangnick quits over transfer
Rangnick's decision followed the announcement on Saturday that their Brazilian defender Luiz Gustavo is being sold to champions Bayern Munich.
Hoffenheim said on their website that Rangnick would be replaced by his former assistant Marco Pezzaiuoli.
"It's a unique case for a player to be sold without the coach being directly informed," Rangnick was quoted as saying by the Bild newspaper. "That led to my decision."
Dietmar Hopp, the co-founder of software giant SAP who has bankrolled Hoffenheim's rise from obscurity, paid tribute to Rangnick as he played down any differences between the pair.
"The unique success of our progress to the top flight will remain closely connected with Ralf Rangnick," he said on Hoffenheim's website. "He has developed and established an exemplary sporting structure for the club.
"As the project of reaching the top flight was accomplished two years ago, it is understandable that Ralf Rangnick is looking for other challenges."
Rangnick took over the club in 2006 when they were still in the Regionalliga Sud, part of the third tier of German football, and won promotion to the second division in his first full season.
They were promoted to the Bundesliga the following 2007/08 season and have been there since. In 2009, Hoffenheim, originally from the village of Sinsheim, moved to a new 30,000 capacity stadium, the Rhein-Neckar Arena.
Hopp has been backing the club since the 1990s when they were an amateur side. Hoffenheim are eighth in the Bundesliga with 25 points from 17 games.