USA authorities sued Mr Musk for misleading investors and as a result Tesla and Mr Musk were each required to pay a fine of $20m.
The move scotches reports that James Murdoch might have been appointed to the job.
Musk said in August he was considering taking Tesla private in a $420 a share and that he had secured funding for a deal that was later scuttled but attracted scrutiny from several government agencies.
Tesla said Denholm will be serving as Chair on a full-time basis and that she will temporarily step down as Chair of the company's audit committee until she leaves Telstra. The financial regulator accused Musk of fraud and misleading investors, and fined him and the company $20m each.
In the settlement, the SEC pulled back from its demand that Musk, who is synonymous with the Tesla brand, be barred from running Tesla, a sanction that many investors said would be disastrous.
Telstra said she would be leaving her CFO role in the coming months.
The spokeswoman also said Tesla was actively looking for two additional independent directors.
Tesla, which has never reported an annual profit, also came under strain over production schedules for its Model 3 electric vehicle, its newest auto aimed at a wider market.
Denholm has been on the Tesla board as an independent director since 2014 and has had senior roles at other Silicon Valley technology companies including Juniper Networks, where she was chief financial officer, and Sun Microsystems, as well as Japanese carmaker Toyota.
"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", Denholm said according to a statement issued by the vehicle maker.
"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", it quoted her saying.