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.
Ms Denholm, who has spent four years on Tesla's board, is chief financial officer and head of strategy at Telstra, Australia's biggest telecommunications company.
"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", she said in a statement.
Denholm had already served as a member of the Tesla board since 2014. She was appointed as Telstra's CFO in July.
The US Securities and Exchange Commission had charged Musk with securities fraud, alleging that he misled investors when he tweeted on August 7 that he had "funding secured" to privatize the electric automaker at $420 a share, a substantial premium over its share price at the time.
Mr Musk, Tesla's controversial co-founder, resigned as head of its board in September.
Tesla is searching for two more independent directors.
Under that settlement he and Tesla each had to pay a $20 million fine but Musk was allowed to stay on as CEO. 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.
"I look forward to working even more closely with Robyn as we continue accelerating the advent of sustainable energy", he added.
Tesla has seen months of turbulence since Musk's infamous tweet. Musk later tweeted that this was "incorrect".