Elon Musk is to step down as chair of Tesla for three years and pay a fine after reaching a deal with the US financial regulator over tweets he made about taking the firm into private ownership.

Under the settlement Musk would remain as chief executive but must leave his other post within 45 days. Both he and the company will each pay a $20m (£15.3m) fine.

The entrepreneur has overseen two tumultuous months for the car company that battered Tesla’s share price and Musk’s reputation. Last Friday Tesla’s share price was down close to 14% as investors lost confidence.

The Securities and Exchange Commission (SEC) filed a suit in New York accusing Musk of fraud last week, alleging that the tweets about financing for a go-private plan he abandoned just weeks later had no basis in fact, and said the market chaos that ensued hurt investors.

In his tweet in August he said he was considering taking Tesla off the stock market and into private ownership and had “funding secured” for the proposal, which would value Tesla at $420 a share.

Under the terms of the deal, Musk would also have to comply with the company’s communications procedures when tweeting about the firm.

The settlement reached on Saturday does not go as far as the regulator initially demanded when it said that Musk should be barred from running Tesla, a sanction that many investors said would be disastrous for the loss-making electric carmaker.

The SEC charged Tesla with failing to have required disclosure controls and procedures for Musk’s tweets. The SEC said the company had no way to determine if his tweets contained complete and accurate information.

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.