This comes on the back of the decision by the Securities and Exchange Commission (SEC) to sue Mr Musk for alleged securities fraud on Thursday.
The new deal reached on Saturday means that Musk will remain as Chief Executive Officer of electronic car maker Tesla but will relinquish his chairman title for three years and pay a $20m fine.
Musk has 45 days to leave his role as Tesla chairman and will also have to comply with company communications procedures when tweeting about the firm, news site BBC reports.
In August this year, Musk tweeted that he was considering taking Tesla off the stock market and into private ownership.
He said he had secured funding to take Tesla private at $420 a share, and this caused a rise in the company’s stock briefly which later fell again.
But the SEC claimed that he misled investors, adding that Musk had not secured the funding.
“In truth and in fact, Musk had not even discussed, much less confirmed, key deal terms, including price, with any potential funding source,” the regulator said.
Musk called the SEC’s suit “unjustified.”
“I have always taken action in the best interests of truth, transparency and investors,” he said.
“Integrity is the most important value in my life and the facts will show I never compromised this in any way.”
Reports by CNBC said that the SEC filed the suit on Thursday after Musk refused an earlier settlement offer.
Under that deal, Musk would have had to pay a “nominal fine” and leave his role as chairman for two years but he chose not to accept the terms “because he felt that by settling he would not be truthful to himself,” the news site said.
The SEC had also initially sought to ban Musk from working on the board of any publicly traded company, but he will now be able to stay on as Tesla’s CEO under the new deal.
Meanwhile, a new “independent chairman” for the company will be appointed, who will preside over the company’s board.
Some analysts have expressed surprise that the SEC agreed to let Musk stay on as chief executive but exit the chairman role as it will in no way limit his power within the company.
For others, removing him as CEO will have dire consequences on Tesla’s share price and, therefore, harm investors.
Musk is the 25th richest person in the world, according to Forbes, which estimates his net worth to be $19.7 billion.
Before moving to Tesla and rocket company SpaceX, the business magnate and investor amassed a lot of wealth from online payments firm PayPal.
He has recently come under heavy criticism after he was found appearing on a podcast while smoking marijuana in California, causing shares in Tesla to fall more than nine per cent.
The 47-year-old is also being sued for defamation following allegations he made against a British driver involved in the Thai cave rescue.