Dortmund chief executive Hans-Joachim Watzke told a lunchtime press conference that the club had agreed to release him early from his contract.
The charismatic German has long been linked with a job in the Barclays Premier League and Manchester City have been installed as favourites to land the highly-rated coach.
The 47-year-old has spent seven years at Dortmund, during which time he won two Bundesliga titles, the DFB-Pokal and reached the Champions League final.
Klopp faced the media, along with Watzke and the club’s sporting director Michael Zorc.
Klopp said he had no concrete plans in place for the future, but stressed he had no plans to take a sabbatical from the game.
The coach also said his decision was not due to Dortmund’s struggles this season. The club have battled it out at the bottom end of the league for much of the campaign and currently sit 10th.
Zorc thanked Klopp for all he had achieved in his seven years at the club, saying: “We have written football history with you, Jurgen. You have given the club much energy and optimism.”
An emotional Klopp spoke with a clearly heavy heart, having embraced Watzke at the start of the press conference.
He has transformed the team since taking over from Thomas Doll in 2008 after making his name at Mainz, the club where he spent his entire playing career.
But Watzke said they had held talks over the last few days on Klopp’s request and come to a decision.
Klopp said: “I have in the last weeks and days asked myself if I was still the right manager and I wasn’t sure. I couldn’t answer with a yes.”
Arsenal have previously been suggested as a possible destination for Klopp, but it is understood the Gunners remain fully behind current manager Arsene Wenger, who still has two seasons left on a contract extension signed last summer.