The US Securities and Exchange Commission had charged Musk with securities fraud, alleging that he misled investors when he tweeted on August 7 that he had "funding secured" to privatize the electric automaker at $420 a share, a substantial premium over its share price at the time.
Robyn Denholm, the finance chief of Australian telecoms firm Telstra, takes over from the electric auto maker's founder, who remains chief executive.
"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.
Enlarge / Robyn Denholm is the new chair of the board at Tesla.
Tesla weathered a rocky few months in the wake of Musk's tweets that he had "funding secured" for a deal, later scuttled, to take Tesla private. Tesla is searching for two more independent directors.
Mr Musk, Tesla's controversial co-founder, resigned as head of its board in September.
Prior to her appointment, she has served as an independent board director prior to since 2014, Tesla added.
For one, Musk was hit with shareholder lawsuits and an SEC investigation over his tweets about taking the company private. Tesla has to employ or designate a securities lawyer to review messages that senior officers send through Twitter and other social media. Musk and Tesla each had to pay a $20 million penalty under the September deal with the SEC, and he can not return as chairman for three years. She was chief financial and operations officer at Juniper Networks for nine years, and worked at Sun Microsystems.
Shares began to rise after the car-maker reported its largest quarterly profit in the company's history and closed at $348.16 a share yesterday. 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".