Elon Musk must pay a $20 million fine and step down as chairman of Tesla's board to settle securities fraud charges brought by the Securities and Exchange Commission last week. He will remain as the car maker's CEO.

Tesla will also pay an additional $20 million fee; the $40 million total will be distributed to harmed investors, the SEC said Saturday. Neither Musk nor Tesla are admitting any wrongdoing.

At issue is an Aug. 7 tweet from Musk that said he was "considering taking Tesla private at $420" and asserted that he'd secured funding for the move. "Shareholders could either to sell at 420 or hold shares & go private," he wrote in a follow-up tweet.

According to the SEC, however, "Musk knew that the potential transaction was uncertain and subject to numerous contingencies. Musk had not discussed specific deal terms, including price, with any potential financing partners, and his statements about the possible transaction lacked an adequate basis in fact."

The tweet caused Tesla's stock price to jump by over 6 percent that day "and led to significant market disruption," the agency says.

Tesla said in 2013 that it would use Musk's Twitter account to announce "material information about Tesla," but the company didn't really have any rules for how that might work or comply with SEC rules. As part of the SEC settlement, Tesla must "put in place additional controls and procedures to oversee Musk's communications."

Musk has not tweeted about the SEC settlement.

In addition, Tesla must replace Musk with an independent chairman; Musk can't be considered as chairman for at least three years. Tesla must also add two new independent directors to its board.

"The total package of remedies and relief announced today are specifically designed to address the misconduct at issue by strengthening Tesla's corporate governance and oversight in order to protect investors," Stephanie Avakian, co-director of the SEC's Enforcement Division, said in a statement.