Former Liverpool stopper Reina, 32, was deputy to Manuel Neuer at Bayern where he made three league appearances and collected a Bundesliga winner's medal.
"Pepe Reina asked us to release him from his contract, because he has the chance of regular first-team football as first-choice Napoli goalkeeper," Bayern's deputy chairman Jan-Christian Dreesen said on their website (www.fcbayern.de).
"As a player, but especially as a person, he fitted in outstandingly with our team, so we naturally agreed to his request," he added of a player who was on loan at Stadio San Paolo in 2013-14 before joining Bayern.
Reina, who was born in Madrid, started out playing for Barcelona's youth team and spent five years in La Liga, two with Barca, where he made 30 appearances, and three with Villarreal, who he played for 109 times.
In 2005 he moved to Liverpool where he spent eight seasons and played 285 Premier League games while featuring twice at the 2006 World Cup in Germany for Spain who have given him 33 caps.
At Liverpool he won the European Super Cup in 2005, the FA Cup in 2006 and the League Cup in 2012.
With the Spanish national team he won the World Cup in 2010 and two European Championships in 2008 and 2012 plus third place in the 2009 Confederations Cup and second spot in 2013.
(Writing by Ken Ferris; editing by Greg Stutchbury)
