Ms Denholm, who has spent four years on Tesla's board, is chief financial officer and head of strategy at Telstra, Australia's biggest telecommunications company.
The announcement comes ahead of a November 13 deadline that was part of Musk's settlement with the U.S. Securities and Exchange Commission to end claims he misled investors.
Tesla was required to select a new chair of the board as part of a deal between Elon Musk and the Trade and Securities Commission following a tweet that suggested Musk had "funding secured" to take Tesla private.
Musk will help ease the new board director´s transition, Tesla said. The deal required Musk to not serve as chairman for three years. Tesla's shares soared following his comments.
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.More news: At least six injured in shooting at California bar
More news: Priyanka Chopra models two bridal looks during her bachelorette party
More news: Yoga studio shooter was a racist misogynist who found solidarity with 'incels'
Denholm is now chief financial officer at Australian telecoms operator Telstra Corp Ltd and has been an independent director on Tesla's board since 2014. Besides Telstra, her previous experience includes Juniper Network, Sun Microsystems and Toyota.
For one, Musk was hit with shareholder lawsuits and an SEC investigation over his tweets about taking the company private.
Email messages sent to Denholm Thursday were not immediately returned. It was only the third time that Tesla has posted a quarterly profit in its eight-year history as a public company and the first time in two years. The mid-priced Tesla Model 3 was the fifth bestselling passenger vehicle in America, according to the industry analyst Edmunds. The aim is to provide stronger oversight to match Tesla's growing stature and market value.
Neither Musk nor Tesla admitted or denied the SEC's findings as part of the settlement.
Musk resigned as Tesla chairman in October under an arrangement with USA regulators to settle fraud charges stemming from a tweet in which he said he planned to take the company private and had financing to do it.