According to Tesla, she will leave the Australian telco at the end of her six-month notice period.
Denholm has held leadership roles in both Australia and Silicon Valley, including Juniper Networks and Sun Microsystems.
"I believe in this company, 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", Ms Denholm said. 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.
She is now just one of two women on the board of Tesla. A spokesperson at the company told CNBC that Denholm will receive 8,000 stock options each year and a cash retainer of $300,000 once she leaves Telstra. She will assume the chairman's role immediately, the company said.
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.
But Tesla's stock had tumbled by more than 25 per cent before recovering the $7billion loss the SEC lawsuit incurred.
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Prosecutors charged him with premeditated murder and a judge decided on Monday that he will be held in jail without bond. WFTV reported that Ramos allegedly strangled his mother and they got into a fight over a "D" grade he received in school.
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On Twitter Thursday morning, Musk wrote that he has great respect for Denholm.
Corporate governance experts say they would have preferred an outsider with manufacturing expertise be appointed to lead the board, now dominated by people with personal and financial ties to Musk, including his brother. And as a result, a flawless place for someone like CEO Elon Musk to lurk behind the shadows. Since it went public in 2010, Tesla has posted a profit in only two quarters: once in 2013 and again in 2016.
Denholm, who has an undergraduate degree in economics from the University of Sydney and a master's degree in commerce from the University of New South Wales, has worked in senior roles for a number of technology companies.
Musk, who remains Tesla's biggest shareholder and the driving force behind its ambitious plans to reshape electric battery technology and auto transport, tweeted https://twitter.com/elonmusk/status/1060452014642016256 his approval of the appointment.
Even after the settlement was announced, Mr Musk taunted the SEC, calling it the "Shortseller Enrichment Commission" before snidely praising it for "doing incredible work".