Maddon, 60, had led the Rays since 2006 and still had a year remaining on his deal with the franchise.
In a statement, Rays principal owner Stuart Sternberg said he had tried to extend Maddon's stay - but was powerless to stop him leaving.
"Joe Maddon has exercised an opt-out in his current contract, a contract which was not scheduled to expire until after the 2015 season," he said on Friday.
"We tried diligently and aggressively to sign Joe to a third contract extension prior to his decision.
"As of [Thursday] afternoon, Joe enabled himself to explore opportunities throughout Major League Baseball. He will not be managing the Rays in 2015.
"Joe has been our manager for nine seasons, and the foundation of success laid during his tenure endures. We thank him for all that he's meant to the organisation."
Maddon, 60, said he was unaware of the opt-out clause until he was told following the departure of Andrew Friedman to the Dodgers.
"I didn't know anything about [the clause] until Andrew left, because it wasn't even on my radar," Maddon said.
"And I didn't even remember or realise that I had this opt-out clause until I was informed of it. There was a two-week window [to make a decision].
"The word is agonising in trying to come to the terms with the Rays negotiating wise, and I could just see that it wasn't going to get to the point where I thought it was necessary to get to.
"And with that I thought it was the right thing to exercise the option to get out there and explore this opportunity, which is really unique and something that I've never had before."
Friedman left the Rays to become the president of baseball operations at the Dodgers and is a close friend of Maddon's.
But Friedman said the Dodgers were sticking with manager Don Mattingly in 2015.
"As I said last week, Joe and I enjoyed a tremendous relationship working together in Tampa Bay and I wish him nothing but the best wherever his next stop will be," he said.
"However, nothing has changed on our end and Don Mattingly will be our manager next season and hopefully for a long time to come."