Tesla Inc. named Robyn Denholm as its new chairman, replacing Chief Executive Elon Musk as the head of the board with a relative outsider who will face the difficult task of overseeing the maverick billionaire.

Ms. Denholm, the chief financial officer of Australian telecommunications company Telstra Corp., has served on Tesla’s board since 2014 but has fewer ties to Mr. Musk than most of the company’s directors. She takes over as chairman of Tesla effective immediately, Tesla said, and she will continue in her role at Telstra...