John Finnegan is set to replace Chubb chief executive and president Dean O'Hare when he retires on 1 December.
Joel Cohen will also join as non-executive chairman.
Previously, Finnegan was chairman and president of General Motors Acceptance. Cohen was director of the insurer since 1984.
The company faces long-term problems.
Chubb and other insurers havebeen threatened with large claims as litigants that have sued asbestos producers are now successfully moving against the companies that distributed the product.
By some estimates, US insurers will have added $3bn (£1.9bn) this year to the $15bn (£10bn) they had set aside to cover asbestos losses.
Chubb was recently forced to more than double its reserves to over $1bn (£640m) to cover asbestos claims .
Thomas Motamed was also promoted to vice-chairman and chief operating officer.