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.