Tesla has weathered a rocky few months in the wake of Mr Musk's tweets that he had "funding secured" for a deal, later scuttled, to take Tesla private.
The appointment comes more than a month after the billionaire had to step down as the electric-car maker's chairman as part of a settlement with US regulators.
Robyn Denholm, the finance chief of Australian telecoms firm Telstra, takes over from the electric vehicle maker's founder, who remains chief executive.
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", the statement from the electric car-maker said.
Denholm had already served as a member of the Tesla board since 2014.
U.S. authorities sued Mr Musk for misleading investors and as a result Tesla and Mr Musk were each required to pay a fine of $20m.
Tesla is searching for two more independent directors.
"Robyn has extensive experience in both the tech and auto industries, and she has made significant contributions as a Tesla board member over the past four years in helping us become a profitable company", said Mr Musk.
She will also be leaving her role as CFO and Head of Strategy at Telstra..
Before moving to Telstra, she worked for Silicon Valley firms Sun Microsystems and Juniper Networks as well as consultants Arthur Anderson and Toyota. "I look forward to working even more closely with Robyn as we continue accelerating the advent of sustainable energy".
Tesla has seen months of turbulence since Musk's infamous tweet.
The settlement in late September with the Securities and Exchange Commission allowed Musk to remain CEO of Tesla but required him to relinquish his role as chairperson for at least three years.
The tweet was one of a number of public statements by Musk that raised questions in the industry about his aptness to lead the company.