Tesla announced Denholm's appointment weeks after the Financial Times reported that James Murdoch, who also sits on Tesla's board, was the frontrunner.
"To ensure a smooth transition during the remainder of Robyn's time at Telstra, Elon will be a resource to Robyn and provide any support that she requests in her role as chair".
"The fact that he can remain CEO is very important for the company".
U.S. authorities sued Mr Musk for misleading investors and as a result Tesla and Mr Musk were each required to pay a fine of $20m. In media interviews he said he often slept on a sofa in the Tesla office and more recently in an online video he briefly smoked marijuana.
Tesla's board, which includes Musk's brother Kimbal, has long come under fire from corporate governance experts for lacking independence and being comprised of Musk loyalists.
Denholm is now the Chair of Tesla's Audit Committee a role she will step away from until her initial 6 month notice period is complete.
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Tesla has appointed Robyn Denholm as its chairwoman after Elon Musk was forced to stand down in a boardroom shake-up at the electric carmaker.
Email messages sent to Denholm Thursday were not immediately returned.
Tesla earned a $311.5 million net profit during the third-quarter, delivering the first step of a promise from Musk to post sustainable profits.
A big jump in Tesla's output of its mass-market Model 3 vehicle powered the breakthrough.
Denholm's appointment is expected to cap months of turbulence for the company.
Tesla's conflict with the SEC began in August, when Musk tweeted that he was taking the auto company private and had "funding secured" at $420 a share.
That alluded to shortsellers, investors who have bet that Tesla shares will fall and who are frequently the subject of Musk´s derision.