As part of the settlement, Tesla will appoint an independent chairman, two independent directors, and a board committee to set controls over Mr Musk's communications under the proposed agreement.
US securities regulators settled a lawsuit against Musk alleging that he made false and misleading statements about plans to take the company private in August.
It alleged that Musk's statements - including the assertion that he had "funding secured" to take Tesla private - "were premised on a long series of baseless assumptions and were contrary to facts that Musk knew".
Billionaire businessman Elon Musk has stepped down as the Chairman of Tesla following a tweet where he claimed he has the funding and investor support to buy the publicly-traded company.
"The $40 million in penalties will be distributed to harmed investors under a court-approved process", the SEC said.
In a follow-up company blog post issued August 13, Musk explained that his assertion of having "funding secured" was based on multiple encounters he had with the Saudi Arabian sovereign wealth fund, where he felt there was "no question that a deal with the Saudi sovereign fund could be closed".
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Tesla did not immediately respond to requests for comment.
"Shareholders with Tesla will be able to go to sleep tonight knowing the Musk will remain at the helm of the company".
"Both sides have pulled back, taken a deep breath and realized that in the interest of the company, its shareholders, they need to put this behind them", said Stephen Crimmins, a former SEC enforcement lawyer who's now a partner at Murphy & McGonigle.
According to the agreement filed on Saturday, Musk must resign as chair within 45 days.
"The resolution is meant to prevent further market disruption and harm to Tesla's shareholders", Peikin added.
Musk has baffled investors with emotional and seemingly erratic media appearances, including one where he appeared to smoke marijuana, and a public battle with a rescuer who helped save a group of boys trapped in a cave in Thailand, whom he termed a "pedo guy".
The company is expected to release quarterly production numbers this week for the Model 3, seen by analysts as crucial to the carmaker's drive to achieve long-term profitability.