Tesla has seen months of turbulence since Musk's infamous tweet.
Ms Denholm is now Chief Financial Officer at Australian biggest telecoms company, Telstra, and already sits on the board of Telsa as an independent director.
Prior to her appointment, she has served as an independent board director prior to since 2014, Tesla added.
Mr Musk agreed to give up the chairmanship last month to resolve claims of fraud brought by U.S. financial regulators.
The settlement requires Tesla to install an independent chairman, among other penalties. In it, Musk said he was considering taking Tesla private at $420 a share - and had funding secured.
The announcement comes after Musk was ousted as board chair in September as part of a settlement with the SEC, which filed a lawsuit against him following an August tweet in which he said he was considering taking the company private, surprising investors, analysts and the board.
He also taken aim at short-sellers, or investors who borrowed shares of Tesla and immediately sold them with the hope that Tesla's share price would fall, a number of times.
Under that settlement he and Tesla each had to pay a $20 million fine but Musk was allowed to stay on as CEO. She was appointed as Telstra's CFO in July.
Tesla, which has never reported an annual profit, also came under strain over production schedules for its Model 3 electric auto, its newest vehicle aimed at a wider market.
She will give up these positions after serving a six-month notice period to take up a full-time chairman position at Tesla.
"To ensure a smooth transition during the remainder of Robyn's time at Telstra, Elon will be a resource to Robyn and provide any support that she requests in her role as Chair", Tesla said in a news release. She also has worked at various technology companies including Juniper Networks and Sun Microsystems and held finance management posts at Toyota Motor Corp.in Australia.