Both he and Tesla will also have to pay a $20m (£15m) fine.
This is important as the SEC's lawsuit against Musk stated he made a series of "materially false and misleading statements" about taking the company private and having secured the funding to do so.
Things could ultimately have been significantly worse for Musk, as the SEC had sought to bar him from serving as an officer or board member of a publicly traded company.
In the tweets to his 22 million followers, he suggested he would take Tesla private at $420 per share - a substantial premium to its trading price at the time.
Iran will have hell to pay: USA national security adviser
Secretary of State Mike Pompeo had said the president would have "strong words" for Iran's leadership. They do not respect their neighbours or borders, or the sovereign rights of nations.
According to the SEC statement, neither Musk nor Tesla admit any wrongdoing.
Musk claimed funding had already been secured for the deal and that the only remaining uncertainty was a shareholder vote.
Musk is now required to step down as chairman of Tesla within 45 days, and he is not permitted to be re-elected to the post for three years. The SEC charged Tesla with failing to have required disclosure controls and procedures for Musk's tweets.
Tesla said in 2013 that it would use Musk's Twitter account to announce "material information about Tesla", but the company didn't really have any rules for how that might work or comply with SEC rules.
It noted that the tweets caused significant market disruption. Tesla must also add two new independent directors to its board.