Tesla has named two independent board directors as part of a September deal with federal regulators to move past the turbulence following chief executive officer Elon Musk's tweet about taking the electric car-maker private.

The company said on Friday Oracle Corp's founder Larry Ellison and Walgreens Boots Alliance's global head of human resources Kathleen Wilson-Thompson joined the board as independent directors, effective December 27. Ellison bought 3 million shares of Tesla earlier this year.

"In Larry and Kathleen, we have added a pre-eminent entrepreneur and a human resources leader, both of whom have a passion for sustainable energy," Tesla said.

Under an agreement with the US Securities and Exchange Commission, Musk agreed to pay a $US20 million ($A28 million) fine and step aside as Tesla's chairman for three years to settle charges that could have forced his exit. Tesla also agreed to pay a $US20 million fine.

Tesla also agreed to appoint an independent chairman, two independent directors and a board committee to control Musk's communications.

A US judge in October approved the deal resulting from Musk's August 7 tweets that he was considering taking the company private and had secured funding, which prompted the SEC to file fraud charges against him.

In November, Tesla named director Robyn Denholm as board chair, fulfilling one of the demands. She joined Tesla as an independent director in 2014 and agreed to step down from her job as finance chief of Australian telecoms firm Telstra.

The stock dropped in September after the SEC accused Musk, 47, of fraud over his "false and misleading" tweets.

The company's shares were up 4.4 per cent at $US330 in early trading on Friday.