Recent court documents show Ms Denholm was paid $US4.9 million ($7 million) as a Tesla director in 2017, compared with total compensation of $2 million at Telstra previous year.
She will temporarily step down as Chair of Tesla's Audit Committee until she leaves Telstra, the company said.
Musk, who has been on Tesla's board since 2004, tweeted in August he was considering taking the company private for $420 per share and had secured funding for a deal that was later scuttled but attracted scrutiny from several government agencies.
The move scotches reports that James Murdoch might have been appointed to the job.
He also taken aim at short-sellers, or investors who borrowed shares of Tesla and immediately sold them with the hope that Tesla's share price would fall, a number of times.
U.S. authorities sued the entrepreneur for misleading investors and he and Tesla were each fined $20m.
Musk had to step aside as chairman for three years and was also fined, but was able to remain Tesla's CEO.
The appointment of Denholm caps months of turbulence for Tesla amid investor demands for stronger oversight.
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But Tesla's stock had tumbled by more than 25 per cent before recovering the $7billion loss the SEC lawsuit incurred.
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.
Telstra said she would be leaving her CFO role in the coming months.
Mr Musk heaped praise on his replacement.
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.
"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.
Bye, Musk. Tesla just announced a new chair to its board.