In the agreement, Musk will resign as Chairman but will remain CEO and also a member of the board.
The shares closed Thursday at US$307.52 before the SEC announced its enforcement action over the tweets, in which Musk said he had "funding secured" to take the company private at US$420 a share. The tweets had no basis in fact, and the ensuring market chaos hurt investors, the SEC said.
As part of a settlement of charges that Mr Musk misled investors, he will no longer sit at the head of the boardroom table.
Tesla must hire an independent chair to oversee the company.
Separately, Tesla agreed Saturday to pay $20 million to settle claims it failed to adequately police Musk's tweet. "The resolution is meant to prevent further market disruption and harm to Tesla's shareholders", said SEC enforcement division co-director Steven Peikin.
The optimistic memo and Musk's near-miss are expected to result in Tesla's shares rallying today.
Tesla is seeking to ramp up production of its Model 3, the mass-market vehicle seen as a key to the automaker's future.
Musk has baffled investors with emotional and seemingly erratic media appearances, including one where he appeared to smoke marijuana, and a public battle with a rescuer who helped save a group of boys trapped in a cave in Thailand, whom he termed a "pedo guy".