Musk will stay on as company CEO but will relinquish his role as company chair for at least three years as part of the agreement, which is still subject to court approval.
The SEC said Musk's statements on Twitter were "false and misleading" and that he had never discussed the plans with company officials or potential funders.
Musk has agreed to pay out the $20 million fine.
Tesla Inc. jumped in pre-market trading after founder Elon Musk settled a lawsuit brought by regulators over his August tweet storm, reassuring investors that he'll still be calling the shots at the electric-car maker struggling to meet production goals.
Likewise, Tesla will pay another $20 million due to its failure to check whether Musk's announcements complied with the law. The SEC said the company had no way to determine if his tweets contained information that must be disclosed in corporate filings, or if they contained complete and accurate information. The tweets had no basis in fact, and the ensuring market chaos hurt investors, the SEC said.
Tesla Motors CEO Elon Musk reveals the Tesla Energy Powerwall Home Battery during an event in Hawthorne, California, U.S., April 30, 2015.
Tesla shares sank last week after the SEC accused Mr Musk of securities fraud, opening up the prospect of a long-drawn out fight that could have seen Tesla lose its leader, undermine its ability to raise capital and cripple operations.
Tesla is seeking to ramp up production of its Model 3, the mass-market vehicle seen as a key to the automaker's future.
"We believe Musk's settlement with the SEC is positive for all stakeholders and should allow TSLA to return its focus to producing quality cars", Baird analyst Ben Kallo said.
But its shares have been hit hard since the SEC filed the lawsuit. Munster pointed out that the terms of the settlement actually works in Tesla's favor, as the appointment of a new, capable Chairman of the Board could help Tesla reach sustainability, as well as become the wake-up call that Musk needs with regards to his behavior online.