The 26-year-old midfielder had been linked with a move to Liverpool but will now join Hannover’s Bundesliga rivals in the summer for an undisclosed fee set out in the player’s contract.
“Hannover had made Lars a very good offer, but we have got to respect his choice to leave in the summer,” said Hannover’s director of sport Dirk Dufner.
“There is no doubt in our minds that Lars will give his best possible performance for us until his last game for Hannover.
“He is a top professional with a flawless character.”
Stindl joined the Reds from Karlsruher in 2010 and became the club’s captain following the retirement of Steven Cherundolo last year.
He helped Hannover qualify twice for the Europa League during his time at the club, in which he has made 154 appearances.
“Since I have made up my mind, I wanted to announce it without delay and be open and honest,” Stindl said.
“I will give all I have got in the games that remain to ensure that Hannover secure their place in the Bundesliga next season.
“I have chosen to take the next step in my career, but until the end of the season it is all about giving my best performance so that Hannover stay in the Bundesliga.”