Mr Musk and Tesla settled with the United States Securities and Exchange Commission in September after the agency sued for fraud.
The settlement requires Tesla to install an independent chairman, among other penalties.
The move scotches reports that James Murdoch might have been appointed to the job.
But his impulsive streak caused him trouble when he tweeted in August that he had "funding secured" for taking Tesla private.
U.S. authorities sued the entrepreneur for misleading investors and he and Tesla were each fined $20m.
The settlement required Tesla and Mr Musk to pay a fine of $20 million each and for Mr Musk to give up his chairman role for three years.
It added that she would leave her position as the CFO and Head of Strategy at Telstra, Australia's largest telecommunications company once her six-month notice period there was over.
Weeks later, Mr Musk backed away from the plan, citing investor feedback. Tesla is searching for two more independent directors.
Ms Denholm, who has been on Tesla's board since August 2014, became Telstra CFO in July. The mid-priced Tesla Model 3 was the fifth bestselling passenger auto in America, according to the industry analyst Edmunds.
The carmaker last month quieted some critics after it reported a net profit, positive cash flow and wider-than-expected margins in the third quarter, delivering on Musk's promise to turn the company profitable. "I believe in its mission and I look forward to helping Elon and the Tesla team achieve sustainable profitability and drive long-term shareholder value", Denholm said in a statement.
Before moving to Telstra, she worked for Silicon Valley firms Sun Microsystems and Juniper Networks as well as consultants Arthur Anderson and Toyota.