Tesla said Ms Denholm, who is already chair of Tesla's audit committee, will step down from that role when she leaves Telstra.
The settlement requires Tesla to install an independent chairman, among other penalties.
The move scotches reports that James Murdoch might have been appointed to the job. Musk and Tesla settled with the US SEC in September after the agency sued for fraud.
Tesla had until November 13 to name an independent board chairman under the settlement with the US Securities and Exchange Commission, which said Musk's tweets about taking the company private were fraudulent and that the billionaire could retain his role as CEO but should quit as chairman.
That alluded to shortsellers, investors who have bet that Tesla shares will fall and who are frequently the subject of Musk´s derision.
The appointment of Denholm caps months of turbulence for Tesla amid investor demands for stronger oversight.
Two days after the lawsuit, Musk reached a settlement with the commission, agreeing to a personal fine of $20 million, a separate $20 million fine by Tesla and his resignation as chair. The mid-priced Tesla Model 3 was the fifth bestselling passenger auto in America, according to the industry analyst Edmunds.
"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", she said in a statement.
A Tesla spokesman said Ms Denholm would receive an annual cash retainer of $300,000, with $8000 in stock options annually.
Denholm will leave the Australian telco following a six-month notice period, during which her predecessor Elon Musk will provide her support to "ensure a smooth transition", according to the statement.
Aside from her work at Telstra, she has also spent time at technology majors including Juniper Networks and Sun Microsystems.