"We have reached an agreement - we just have to sign the deal," said Bayern's general manager Uli Hoeness from the club's winter camp in Dubai.
29-year-old Olic, whose contract with Hamburg expires in June, is to sign a three-year contract. A sometime target for Juventus and Liverpool, he has spent two seasons in northern Germany since arriving from CSKA Moscow, scoring 25 goals, including six in Hamburg's current campaign.
Olic has won 61 Croatian caps, scoring 11 goals for his country. The striker will vie with German international Miroslav Klose and Italian star Luca Toni for a starting place in Bayern's attacking force.
The acquisition of Olic will offset the loss of German forward Lukas Podolski, who has not settled since a 2006 move from Cologne. Cologne intend to use their first option on Podolski despite interest from assorted big-name European clubs.