Robyn Denholm, the finance chief of Australian telecoms firm Telstra, takes over from the electric auto maker's founder, who remains chief executive.
The settlement requires Tesla to install an independent chairman, among other penalties.
Musk, who has been on Tesla's board since 2004, tweeted in August he was considering taking the company private for $420 per share and had secured funding for a deal that was later scuttled but attracted scrutiny from several government agencies.
The announcement scotches reports that James Murdoch was the frontrunner for the job.
Tesla agreed to hire an independent chairman, appoint two non-executive directors and establish a board-level committee to oversee Mr Musk's communications as part of a settlement with the US Securities and Exchange Commission.
The SEC accused him of manipulating the market and sued him in late September for making "false and misleading" statements to investors.
In the settlement, the SEC pulled back from its demand that Musk, who is synonymous with the Tesla brand, be barred from running Tesla, a sanction that many investors said would be disastrous.
Musk had to step aside as chairman for three years and was also fined, but was able to remain Tesla's CEO. However, the carmaker made what Mr Musk called an "historic" profit in the most recent quarter.
"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.
Bye, Musk. Tesla just announced a new chair to its board. 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.