The announcement comes after Telsa had until November 13 to name an independent board chairman under its agreement with the Securities and Exchange Commission.
Critics of Tesla's board have said members lack independence and are too closely allied with Musk, many through financial deals.
The settlement with the securities watchdog required Musk and Tesla to each pay $20 million in fines (€17.5 million).
The 55-year-old Australian will temporarily step down as chair of Tesla's audit committee until she quits Telstra.
Denholm has served on the Tesla Board as an independent director since 2014.
Denholm, who has only been in the Telstra CFO job for a little more than a month, said she plans to devote herself full time to Tesla when her obligations to the Melbourne-based telecommunications company are complete.
Denholm has auto sector and Silicon Valley experience.
Denholm, who is also Telstra's head of strategy, has worked at various technology companies including Juniper Networks and Sun Microsystems and held finance management posts at Toyota Motor Corp.in Australia. Since January 2017, she has also been chief financial officer of Australian telecoms firm Telstra.
On Twitter Thursday morning Musk wrote that he has great respect for Denholm.
Despite the scandals, Tesla made a profit of $312m in the third quarter, well ahead of Wall Street forecasts, with revenues of $6.8bn.
Apart from appointing a new chairman under the settlement, Tesla was required to appoint two new independent members to its board.
Ceding the role of chairman was a condition of the accord Musk reached with the SEC in September to settle fraud charges related to his tweets on taking the company private.
The appointment of Denholm caps months of turbulence for Tesla amid investor demands for stronger oversight.
That alluded to shortsellers, investors who have bet that Tesla shares will fall and who are frequently the subject of Musk´s derision. But even after the settlement was announced, Musk taunted the agency, calling it the "Shortseller Enrichment Commission" before snidely praising it for "doing incredible work".