Denholm will leave the Australian telco following a six-month notice period, during which her predecessor Elon Musk will provide her support to "ensure a smooth transition", according to the statement.
Australian telecommunications executive Robyn Denholm brings much-needed financial and auto industry expertise to her new role as Tesla's board chairwoman, but her biggest challenge is whether she can rein in a CEO with a proclivity for misbehavior.
Executive recruiter Patricia Lenkov, however, said that Denholm likely was not the right pick for the job, arguing Tesla needed a figure with more experience dealing with strong founders.
She is now just one of two women on the board of Tesla. She also has held financial management posts at Toyota Motor Corp.in Australia.
Elon Musk stepped down as chair of Tesla last month after the U.S. Securities and Exchange Commission (SEC) sued him for his "false and misleading" claims of potential taking Tesla private - now known as the 420 tweet.
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She has been a member of the board at Tesla since 2014 and will have the task of overseeing Musk who remains as CEO. Telstra is the largest telecommunications company in Australia.
As part of Musk's settlement with the SEC, Tesla also is supposed to monitor Twitter posts that he makes if they have to do with company news that could impact the value of investors' shares in the company.
Inquiries to the automaker by Automotive News have prompted Tesla to deny Musk's involvement in the account, responding with a simple "No."The Drive's own inquiries have ushered the same response". Since it went public in 2010, Tesla has posted a profit in only two quarters: once in 2013 and again in 2016.
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.
Musk had agreed to step down as chairman as part of a deal he struck with the SEC to settle charges that he manipulated the stock price when he sent that infamous "funding secured" tweet in August. The money will go to shareholders who lost money following Musk's tweet.
The SEC settlement required the new chair to be an independent director. But even after the settlement was announced, Musk taunted the agency, calling it the "Shortseller Enrichment Commission" before snidely praising it for "doing incredible work".