Tesla released a statement a short time ago saying that Denholm had handed in her notice at Telstra and would take on the full-time chair role "effectively immediately".
That deal required Musk to step aside as head of the board for three years in favor of an independent chairman. Musk and Tesla settled with the Securities and Exchange Commission (SEC) in September after the USA agency sued for fraud.
The announcement scotches reports that James Murdoch was the frontrunner for 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.
Its shares soared following his comments but weeks later Mr Musk backed away from the plan, blaming feedback from shareholders.
Ariana Grande Teases Wedding-Themed ''Thank U, Next'' Performance
The split happened in the wake of the overdose death of another of the singer's ex-boyfriends, Mac Miller , in September 2018. The tracks included Cadillac and Champagne, thought to be versions of Ariana's previously unreleased songs.
The SEC accused him of manipulating the market and sued him in late September for making "false and misleading" statements to investors.
Tesla has seen months of turbulence since Musk's infamous tweet. Most commenters approve of Tesla's decision though there are a few upset by it.
"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.
Musk cited Denholm's long experience in the tech and auto industries as strong advantages and said in a statement that he looked forward to working with her.
Denholm has been on the Tesla board as an independent director since 2014 and has had senior roles at other Silicon Valley technology companies including Juniper Networks, where she was chief financial officer, and Sun Microsystems, as well as Japanese carmaker Toyota.
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