The company also accepted a $20m fine, despite not being charged with fraud.
Musk can't be chairman for at least three years, although Tesla can request extensions for the board and chairmanship changes, according to court filings.
A federal judge has approved Musk's settlement with the SEC over securities fraud allegations. The agreement comes at a time when the auto maker is ramping up production and deliveries of its Model 3 vehicle and needs to reassure customers its outlook is sustainable and profitable.
Judy Burns, an SEC spokeswoman, didn't immediately respond to a request for comment. Despite the gains, the stock is still down more than 20 percent since August 6, the day before Musk said on Twitter he would take the company private and claimed he had secured funding to do so.
The US Department of Justice (DOJ), which has the authority to press criminal charges, has also questioned the company about Mr. Musk's Tweets, the company said this month.
Earlier this year, Elon Musk tweeted a joke product for April Fools Day - a Tesla branded tequila. The SEC quickly opened an investigation by questioning Musk, Tesla's board and other executives. Tesla has until November 13 to appoint an independent chairman.
Days after of the settlement agreement, Musk shot off a tweet referring to the SEC as the "Short Seller Enrichment Commission" and sarcastically praising the regulator's work. Nevertheless, less than 40 minutes after his tweet about Your Name, Musk tweeted the message "It is time to create a mecha".
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