Musk and Tesla settled with the Securities and Exchange Commission (SEC) in September after the US agency sued for fraud.
Apart from appointing a new chairman, Tesla was required to appoint two new independent members to its board.More news: Sri Lanka president prolongs political standoff
The move scotches reports that James Murdoch might have been appointed to the job.
Tesla has endured a hard few months, following comments on social media in early August made by the firm's founder, Elon Musk, suggesting he had "funding secured" for a deal to take Tesla private. Tesla's shares soared following his comments. The financial regulator accused Musk of fraud and misleading investors, and fined him and the company $20m each. Mr Musk was also obliged to relinquish his role as chairman for three years.
She will take on the full-time role at Tesla after serving a six-month notice period at the Australian firm.More news: First Muslim women in Congress: Rashida Tlaib and Ilhan Omar
In the settlement, the SEC pulled back from its demand that Musk, who is synonymous with the Tesla brand, be barred from running Tesla, a sanction that many investors said would be disastrous.
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.
An Australian, Denholm is Telstra's chief financial officer and head of strategy and already has served on Tesla's board as an independent director.More news: 'Breaking Bad' movie in the works by Vince Gilligan
"I believe in this company, 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", Ms Denholm said. She also has worked at various technology companies including Juniper Networks and Sun Microsystems and held finance management posts at Toyota Motor Corp.in Australia.