The announcement Tuesday comes one day after Goldman Sachs named Oppenheimer as one of its 13 board members.
Oppenheimer, who has been CFO for the past decade, will begin transferring responsibilities to Luca Maestri in June.
Apple CEO Tim Cook says the company knew Maestri would ultimately succeed Oppenheimer when it recruited him as corporate controller a year ago. Maestri has more than 25 years of experience in senior financial management.
He has served as CFO at both Nokia Siemens Networks and Xerox.
Oppenheimer joined Apple in 1996 as controller for the Americas.
Apple Inc. is based in Cupertino, California.