She's now chief financial officer and head of strategy at Telstra, an Australian telecommunications company.
Denholm, one of two female directors on the nine-member board, assumes her new position immediately, Tesla said.
The settlement requires Tesla to install an independent chairman, among other penalties. Musk and Tesla settled with the Securities and Exchange Commission (SEC) in September after the USA agency sued for fraud.
The move scotches reports that James Murdoch might have been appointed to the job.
Musk stepped down as Tesla chair in late September as part of a settlement with the US Securities and Exchange Commission (SEC) stemming from a tweet that US authorities alleged had misled investors.
Under that settlement he and Tesla each had to pay a $20 million fine but Musk was allowed to stay on as CEO.More news: Indonesian Plane Grounded as Passengers Refuse to Fly Because of Durian Fruit
Tesla says Denholm will leave Telstra after her six-month notice period with the company is complete.
But Tesla's stock had tumbled by more than 25 per cent before recovering the $7billion loss the SEC lawsuit incurred.
"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.
"We are undertaking a search for a new chief financial officer and will provide an update on a replacement appointment as soon as possible", Mr Penn 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.
Musk said: 'Robyn has extensive experience in both the tech and auto industries, and she has made significant contributions as a Tesla Board member over the past four years in helping us become a profitable company.