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."
