Tesla's showroom in Paramus, New Jersey, was closed by 8 p.m. local time Sunday.
The settlement will stand post a court approval in which Tesla and Musk neither admit nor deny the charges levied by the SEC.
Lawyers said the settlement and size of the fine might give more ammunition to short-sellers pursuing separate cases against Musk for manipulating company shares through the August 7 tweet, as well as to a probe by the Justice Department.
The electric vehicle maker is expected to report third-quarter production numbers on Tuesday, following a period of turbulence, including a run-in with securities regulators that culminated in Musk being ousted as Tesla's chairman and hit with a multimillion-dollar fine.
According to the settlement, Tesla and Musk will pay $20m each to financial regulators and Musk will step down as chairman but remain as chief executive.
Tesla shares fell more than 1 percent in recent trading Tuesday.
Even after the stock's slide from last year's peak, Tesla is valued at $45.2bn in the stock market.
It's not a bad outcome for Musk and Tesla, considering the potential implications of his August 7 tweet, where Musk said he was considering taking the company private, at $US420 a share, and had "funding secured". In addition to appointing an independent chairman, Musk will be ineligible to be re-elected as chairman for three years.
Moreover, Both Tesla and Musk will pay $20 million in fines that will be distributed in a court-approved process to the investors that were potentially harmed by Musk's Twitter activity.
Elon Musk hasn't been one to shy from controversy.
Some highlights: The company said it delivered more than 55,000 Model 3 sedans during the quarter, a 10th of those in the last week of the quarter.
After Musk settled over the weekend, Tesla surged on Monday and closed up 17%. Musk is Tesla's largest investor, holding a 20-percent stake in the company. The basis of the SEC's suit was that Elon didn't have funding secured at all and was potentially misleading investors. As Tesla's largest shareholder, Musk is likely to retain a seat on the board and have influence in determining his successor as chair.