Tesla chief executive Elon Musk agreed on Saturday to step down as chairman of the electric car maker he founded, an unexpected resolution to a lawsuit filed by the Securities and Exchange Commission 48 hours earlier that threatened to throw Tesla into unprecedented chaos.

The SEC sued Musk on Thursday for allegedly lying to investors when he tweeted last month that he had “funding secured” to take Tesla private. It sought to ban the impulsive billionaire from serving as chief executive of any public company.

As part of the settlement, Musk will pay a $20 million fine. Tesla will separately pay another $20 million, add two new independent directors to its board, and monitor more closely Musk’s public communications — the source of many of the scandals that have roiled the ambitious but unprofitable company this year.

The conditions of the agreement “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.

Musk and Tesla were not required to admit to any wrongdoing as part of the settlement. Tesla declined to comment on the settlement.

Reacting to the lawsuit earlier in the week, Musk said the SEC’s “unjustified action” left him “deeply saddened and disappointed.” “Integrity is the most important value in my life, and the facts will show I never compromised this in any way,” he said.

The deal announced Saturday was all the more surprising because the SEC had offered similar terms two weeks ago after conducting an investigation that was unusually quick.

Musk abruptly rejected that initial settlement earlier last week, people familiar with the matter said, prompting the SEC to file civil suit Thursday afternoon.

Musk, meanwhile, hired several high-powered attorneys to prepare a defense, appearing to gear up for the fight of his career.

But Tesla’s stock tumbled more than 15 percent following the SEC lawsuit, reflecting the degree of risk associated with Musk’s leadership of the car maker in jeopardy. It is unclear why Musk, who rarely backs down from a fight, changed his mind.

It was “likely due to pressure from investors,” said Michelle Krebs, executive analyst at Autotrader. Given the potential penalties they faced if the case had gone to trial, “Musk and Tesla got lucky. ... Still, a reckless tweet cost a lot of money — the $20-million tweet.”

Musk stunned global financial markets on Aug. 7 when he issued tweets saying he had the “funding secured” to take his automaker private. Musk said the take-private deal was all but guaranteed, sending the Silicon Valley automaker’s stock soaring by nearly 11 percent.

Then, after 17 days, Musk announced that he would not pursue the deal, leading the stock to plunge amid growing skepticism over the company’s long-term prospects.

But federal securities regulators say his statements were deceptive. Following its investigation, the SEC said the deal “was uncertain and subject to numerous contingencies.”

The settlement is a big victory for the SEC, which faced one of its most high-profile fights in years if the case had gone to trial. Even if the jury found the evidence of fraud convincing, legal experts said, they could have been easily charmed by Musk.

Under the settlement, which is subject to court approval, Musk will resign as chairman of the automaker within 45 days and be barred from that position for three years.

Stepping down as chairman is potentially humbling for Musk, 47, who is currently Tesla’s chairman, chief executive and largest shareholder, with a roughly 20 percent stake in the company. He oversees virtually all of the company’s development, engineering and design.

He also commands a vast audience on Twitter, where he has more than 22 million followers, which Tesla agreed to monitor more closely under the settlement. Musk must now have the company sign off on any written statements, including on Twitter, that could be deemed material.

The settlement ends one potential nightmare for the company.

Some investors have worried about how the electric car company would fare without Musk’s vision and tenacity.

But other stumbling blocks remain. Tesla faces several shareholder lawsuits tied to the Aug. 7 tweet and the Justice Department is also investigating the issue.

Tesla also remains under financial pressure. It has endured months of production problems and an exodus of top executives as it faces down more than $10 billion in lingering debts.