Tesla and Mr Musk will pay $20 million each to financial regulators. Tesla was hit with a $20 million fine of their own. The SEC's lawsuit charged that the tweet, which caused Tesla's shares to jump, was misleading because he did not actually have the funding lined up for such a move.
The settlement involved a hefty fine worth a total of $40 million, as well as Musk's resignation as Chairman for Tesla's Board of Directors, but it did allow him to keep his post as CEO.
Tesla's shares plummeted around 14 percent on Friday over concerns about the company's future after the announcement of the fraud charges against Musk, which were a fresh blow to the mercurial Silicon Valley entrepreneur and his company.
Munster said the settlement was the best outcome for all involved. He's Tesla's largest shareholder, with a 20 percent stake.More news: Sturridge's verdict on sensational strike at Chelsea
Even after the stock's slide from last year's peak, Tesla is valued at $45.2 billion in the stock market.
He's made these assurances in large part due to progress Tesla has made in producing more Model 3 sedans - the first electric vehicle Tesla has tried to mass-manufacture.
From the beginning of this case, the SEC requested as a penalty that Elon Musk had left the position of chairman from the board of Tesla, something that has now been achieved.
"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.More news: Markets to Elon Musk: Stop messing around and settle with SEC
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.
Musk said he later decided against the plan.
"The resolution is meant to prevent further market disruption and harm to Tesla's shareholders", Steven Peikin, co-director of the SEC's Enforcement Division, said in the statement. "At the same time, there will be appropriate restraints in place".
Musk invited wrath in August when he falsely claimed on Twitter that he had secured funds for a multi-billion dollar buyout of Tesla, leading its share price to swell and creating huge losses for "short-selling" investors who had bet against the firm.More news: Paul Pogba May Cost Far More Than Barcelona Are Capable Of Spending
Gore has previously noted his admiration for Tesla and Musk.