Ms Denholm is now Chief Financial Officer at Australian biggest telecoms company, Telstra, and already sits on the board of Telsa as an independent director.
Apart from appointing a new chairman, Tesla was required to appoint two new independent members to its board.
Mr Musk and Tesla settled with the United States Securities and Exchange Commission in September after the agency sued for fraud.
The move scotches reports that James Murdoch might have been appointed to the job.
Tesla had until November 13 to name an independent board chairman under its agreement with the Securities and Exchange Commission, which said Musk's tweets about taking the company private were fraudulent and that the billionaire should quit as chairman but could retain his role as CEO.
He also taken aim at short-sellers, or investors who borrowed shares of Tesla and immediately sold them with the hope that Tesla's share price would fall, a number of times.
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She has only been CFO since October 1 this year, though she joined Telstra in January 2017 as its chief operations officer.
Investors had also called for stronger oversight of Mr Musk after his erratic behaviour attracted attention. The mid-priced Tesla Model 3 was the fifth bestselling passenger vehicle in America, according to the industry analyst Edmunds.
A statement from Ms Denholm said she believed in Tesla and looked forward "to helping Elon and the Tesla team achieve sustainable profitability and drive long-term shareholder value".
Denholm will leave her role as CFO and head of strategy of Telstra once her six-month notice period with the company is complete, Tesla said late on Wednesday.
Besides Telstra, Denholm has worked in other tech companies such as Juniper Networks and Sun Microsystems, and she also worked for Toyota, the statement added.
Electric carmaker Tesla said Robyn Denholm, now CFO at Australian telecoms operator Telstra, will replace Elon Musk as its chair.