The Dutchman, whose current deal expires next year, is expected to commit himself to the European champion in the coming days.
The Netherlands international's current deal is due to expire in the summer of 2015 and both parties have been in talks over a renewal for a number of weeks.
Robben recently stated that he was confident of a prolonged stay at Bayern and he has revealed all that is left to do now is to complete the paperwork.
"We have agreed terms in principle. It's only a matter of signing the new contract now," the Dutch winger is quoted as saying by AZ.
"There are a lot of things going on at the moment, with a lot of games and travels. We might finalize things after the game against Hannover."
The 30-year-old joined Bayern from Real Madrid in the summer of 2009 and has since developed into a key player for the Champions League holder.
He has netted seven goals in 16 Bundesliga games so far this term.