Mr Quinn, currently regional CFO for Swiss Re Americas, will replace the current CFO Ann Godbehere, who is to leave the reinsurance giant.
Swiss Re CEO Jacques Aigrain said of Ms Godbehere: "Her expertise and judgment is widely recognized in the insurance industry, and she stands for excellence in all finance matters."
During her time in the post, she led the acquisitions of GE Insurance Solutions as well as the GE Life UK, which completed last week for $610 million.
Mr Quinn has been with Swiss Re since 1999 and has held the positions of chief accounting officer and business group CFO for financial services.
Peter Forstmoser, chairman of the Swiss Re board, said: "With George Quinn, Swiss Re has nominated an international financial expert with extensive knowledge of Swiss Re and its markets. We are looking forward to working with him in a team."