The terms of the deal were not disclosed. Maddon cited club policy and declined to comment.
"It has always been our policy not to comment on rumors or unconfirmed reports," Rays executive vice president of baseball operations Andrew Friedman said through e-mail.
Maddon, in his fourth season in Tampa Bay, is in the final year of his contract. Overall, he has a 244-283 record entering Wednesday's game, and led the Rays to their World Series run last season, in which the team won 97 games to make the postseason for the first time in the club's history.
He won the 2008 American League Manager of the Year Award, becoming just the fourth manager to finish one vote shy of being a unanimous choice.
Hired in 2005, Maddon previously spent 31 years in the Angels organization, including 12 in the Minor Leagues and 10 as a bench coach for the Angels.
Zach Schonbrun is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.