Tesla has endured a hard few months, following comments Mr Musk made on social media in early August suggesting he had "funding secured" for a deal to take Tesla private.
Robyn Denholm takes over the role from founder Elon Musk, who will remain as Tesla's chief executive.
The tweets sent shares in Tesla soaring to a high of $387.46 a share on August 7.
Major European film company's Twitter account hacked to promote Bitcoin scam
After compromising the verified accounts, the scammers changed the name and profile picture to impersonate Tesla's CEO. In fact, scams became so frequent on Twitter that Musk himself was briefly banned from the social media network.
USA authorities sued the entrepreneur for misleading investors and he and Tesla were each fined $20m.
Tesla, which has never reported an annual profit, also came under strain over production schedules for its Model 3 electric auto, its newest vehicle aimed at a wider market. "We allege that he had not even discussed key deal terms including price with any potential source of funding".
Under that settlement he and Tesla each had to pay a $20 million fine but Musk was allowed to stay on as CEO.
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. In a suit, the SEC originally asked the court to ban Musk from acting as an officer or director of any publicly traded company.
Virat Kohli lashes out at fan
The statement, he writes, is "probably an extension of the nationalist narrative that modern India tries to propagate". One person had said that Kohli is overrated and that it is more enjoyable to watch batsmen from Australia and England.
According to an announcement shared by Tesla, Denholm will serve as the board chairperson on a full-time basis.
Tesla announced that Elon Musk's replacement as its chair will be Robyn Denholm, now chief financial officer at Australian telecommunications operator Telstra. In the meantime, she'll work closely with Musk.
"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.
Besides Telstra, Denholm has worked in other tech companies such as Juniper Networks and Sun Microsystems, and she also worked for Toyota, the statement added.
The midterms show Trump might not get re-elected in 2020
In suburban areas where key House races will be decided, voters skewed significantly toward Democrats by a almost 10-point margin. After all, the strong turnout among Democrats during the primaries suggested a more motivated base than their Republican rivals.
Robyn Denholm has been an independent director on Tesla's nine-member board since 2014.