He will be able to continue as the CEO of Tesla, but cannot be chairman again for three years. Musk will be solely responsible for paying his $20m fine.
Tesla will have to pay a second $20m fine, and appoint two independent directors to replace Musk.
In a statement to TechCrunch on Thursday, Musk said the complaint was "unjustified".
"This unjustified action by the SEC leaves me deeply saddened and disappointed," he said.
"I have always taken action in the best interests of truth, transparency and investors.
"Integrity is the most important value in my life and the facts will show I never compromised this in any way."
Neither Musk nor Tesla admitted or denied the SEC's findings as part of the settlement.
Tesla did not immediately respond to a request for comment and Musk could not immediately be reached for comment.