England goalkeeper Fraser Forster does not know if he will still be at Celtic when they next play in Europe.
Norwich captain Sebastien Bassong has signed a new two-and-a-half-year contract.
The Holland winger had been linked with a move away from the Allianz Arena this summer following reports of a dressing-room bust-up with team-mate Franck Ribery during the Champions League semi-final against Real Madrid.
Chairman Karl-Heinz Rummenigge was always adamant he would stay, though, and Bayern confirmed the 28-year-old has put pen to paper on a new deal on Thursday.Robben scored in Bayern's last-four win over former club Madrid and takes on another one of his old employers in Chelsea in the final.
"I've always emphasised that I feel very, very settled in Munich and at FC Bayern," Robben told the club's official website.
"This is the reason I'm glad to extend my contract ahead of its expiry. FC Bayern is like a family to me. Two of my three children were born in Munich, and my family and I feel at home here.
"This contract extension is also the right decision for me from a sporting perspective. We have a magnificent team, and I'm certain we'll enjoy the maximum possible footballing success in the years to come."
Rummenigge added: "We're extremely pleased that we've extended Arjen's contract a year before its expiry by two further years until 2015.
"Arjen is a very important player for FC Bayern, and also a guarantee of the club's continuing success in the future."
Robben, who won two Premier League titles and an FA Cup in three years at Chelsea between 2004 and 2007, has enjoyed an impressive season, with 17 goals in all competitions.