Neither the company nor Mr. Musk has issued a statement officially commenting on the settlement.

For the past 10 years, since Mr. Musk became chief executive of Tesla, he and the company have been practically synonymous. He is its animating force, setting its strategic direction, making virtually all important decisions and working on nearly every detail of design and manufacturing.

His intensity and ferocious work ethic have led to a wave of executive departures in recent years, and Tesla’s board — which includes Mr. Musk’s brother, Kimbal — is not particularly independent by the standards of most big companies.

The terms of the S.E.C. settlement are intended to change some of that.

Tesla will have to add two independent directors to the board, Mr. Musk will not be able to serve as chairman for three years and the board will have to set up a permanent committee to monitor Mr. Musk’s communications with investors and the public, including his postings on Twitter and other social media. The members of this special committee will be subject to the review and approval of the S.E.C.

Tesla also must “implement mandatory procedures and controls to oversee all of Elon Musk’s communications regarding the company in any format,” according to the settlement. The S.E.C. will monitor to make sure the company is in compliance with those procedures.

Perhaps reflecting the new scrutiny, Tesla put a substantial portion of Mr. Musk’s all-hands email into a financial filing with the commission, dated Sunday.

Some critics of the settlement suggested that the S.E.C. — which sought to bar Mr. Musk from serving as a director or executive of a public company in a lawsuit it filed on Thursday, two days before the settlement — was letting him off easy.

Remarks by the S.E.C.’s chairman, Jay Clayton, about the settlement added to the perception that regulators were making an exception for Mr. Musk, who is so central to Tesla. Mr. Clayton said there was a need to balance penalties for violating securities laws with “the skills and support of certain individuals” who may be important “to the future success of a company.”