The Netherlands international, who joined the club in 2009 from Real Madrid and has a contract until 2013, was unhappy earlier this season after being left on the bench for three games following a slump in form.
The 28-year-old, however, has played a key role in Bayern's recent improvement that has seen them win seven straight games in all competitions as they chase a Champions League-Bundesliga-German Cup treble.
Robben scored the only goal in a 1-0 win over Nuremberg on Saturday to lift the Bavarians within three points of Bundesliga leaders Borussia Dortmund.
"Internally this (contract extension) has been negotiated. I expect Arjen will put his signature to it in the coming period," coach Jupp Heynckes told reporters ahead of Tuesday's Champions League quarter-final return leg against Marseille.
"He is showing how important he is for Bayern. Not only the winning goal this weekend but the way he plays for the team. That is what makes him so valuable for us."
Robben, who joined Real Madrid from Chelsea, has been a target for several top European clubs in recent months.