John Finnegan is set to replace Chubb chief executive and president Dean O'Hare when he retires on 1 December.
Joel Cohen will also come in as non-executive chairman.
Previously, Finnegan was chairman and president of General Motors Acceptance. Mr Cohen was director of the insurer since 1984.
Finnegan said: "I intend to get up to speed quickly on the company and the industry so that we can tackle the issues that face the company head-on."
But the company faces long-term problems. Last week Chubb took a $625 million charge to beef up its asbestos reserves.
Thomas Motamed was also promoted to vice-chairman and chief operating officer and John Degnan and Michael O'Reilly to vice chairman.
