Mr Musk agreed to give up the chairmanship last month to resolve claims of fraud brought by USA financial regulators.
In addition to agreeing to a three-year ban from serving in the job, Musk and Tesla agreed that the company would add two new independent directors to the board by late December. Musk and Tesla each had to pay a $20 million penalty under the September deal with the SEC, and he can not return as chairman for three years.
"While Denholm is technically an independent member of the board, she has been part of the Musk team for some time now and that suggests she will not be up to the task of checking Musk's worst instincts", said Stephen Diamond, a professor of law at Santa Clara University who specializes in corporate governance.
Denholm has auto sector and Silicon Valley experience.
Aside from her work at Telstra, she has also spent time at technology majors including Juniper Networks and Sun Microsystems.
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Prior to working at Telstra, Denholm spent seven years at Toyota in Australia, where she was a senior financial manager. The Australian telecommunications executive will assume the role immediately, the company announced this morning.
On Twitter Thursday morning Musk wrote that he has great respect for Denholm.
Tesla earned a $311.5 million net profit during the third-quarter, delivering the first step of a promise from Musk to post sustainable profits.
The settlement requires Tesla to install an independent chairman, among other penalties. The aim is to provide stronger oversight to match Tesla's growing stature and market value.
Last month Tesla and Musk were both fined $20 million over the tweets in which he claimed he was taking the company private at $420 a share, which the SEC alleges was a number chosen as a joke with his singer girlfriend, Grimes, who introduced him to marijuana.
Neither Musk nor Tesla admitted or denied the SEC's findings as part of the settlement.