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.
United States 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.
'I look forward to working even more closely with Robyn as we continue accelerating the advent of sustainable energy'.
Top proxy advisers Institutional Shareholder Services and Glass, Lewis & Co had each classified Denholm as an "independent" director of Tesla in reports to the carmaker's investors earlier this year.
Tesla Chief Executive Elon Musk stands on the podium as he attends a forum on startups in Hong Kong, China January 26, 2016. It's not clear what convinced her to give up the CFO job at one of the country's most prominent companies for the high-profile task of chairing Tesla.
However, Denholm will have the hard task of of overseeing billionaire Musk who will still be with the firm.
"She was there while all of this was going on", said Charles Elson, director of the corporate governance center at the University of Delaware.
The company had until next week to name the new chairman.
In premarket trade on the Nasdaq exchange Thursday, Tesla's share price was up 0.24 percent at $349.00.
Denholm previously held executive roles at Juniper Networks, Sun Microsystems and Toyota. 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.
The tech whiz Musk is also facing legal action from British diver Vernon Unsworth, who helped to rescue a football team of Thai boys when they became trapped in a cave, by falsely accusing him on Twitter of being a pedophile.
A union-affiliated investor group and officials representing major pension funds in four states have called on Tesla to go beyond the terms of the SEC settlement to fix its corporate governance issues.