Kielholz, currently vice chairman of the Swiss reinsurer, replaces Peter Forstmoser, who steps down on May 1.
The move comes after Swiss Re recorded a full-year net loss of £533m for 2008, and was downgraded by rating agency Moody’s last month. Last month also saw the exit of Swiss Re chief executive Jacques Aigrain.
Kielholz says: “In view of the major challenges confronting us, I have decided to concentrate fully on the Swiss Re chairmanship and to relinquish this role at Credit Suisse.
“Even though the current results are disappointing, the core business is intact. I’m confident that at the annual general meeting, shareholders will support our proposals to strengthen the company’s capital base.”
Credit Suisse chief operating officer Urs Rohner has been appointed as vice chairman of the board, replacing Thomas Bechtler.