Musk did not found Tesla but provided early financing.
Mr Musk, whose tweets on August 7 on a plan to take Tesla private that was later abandoned, has tweeted only once since the settlement was announced - posting a music video by rap group Naughty by Nature.
Two new independent directors will be appointed to the board and a new committee of independent directors will be expected to put in place additional controls and procedures to oversee Musk's communications.
Whoever becomes the new chairperson of Tesla Motors will face the formidable task of reining in Elon Musk, the charismatic, visionary chief executive with an impulsive streak, while also helping Musk achieve his dream of turning Tesla into a profitable, mass-market producer of environmentally friendly electric cars.
Tesla shares rebounded from last week's US lawsuit over Elon Musk's take-private tweets, as a settlement ensured the billionaire will keep calling the shots at the carmaker he's said is on the verge of profitability.
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 shares plummeted 14% on Friday, the biggest drop in nearly five years.
Tesla and Mr Musk will pay $20 million each to financial regulators. In an interview with Politico in 2014, the former vice president said he'd love to own a Tesla.
While the 15-year-old company has never earned an annual profit, Tesla's CEO has vowed it's the verge of making money and stemming cash burn that's exceeded more than $1 billion in recent quarters.
It follows Elon Musk's settlement with the US SEC, which includes an agreement to step down as Tesla chairman within 45 days.
Stephanie Avakian and Steve Peikin, co-directors of the SEC's Enforcement Division, led the talks, taking the reins from the staff attorneys who worked the case, according two people familiar with the matter.
"When companies and corporate insiders make statements, they must act responsibly", SEC Chairman Jay Clayton said.
He arrived at the $420 a share figure by assuming a 20 percent premium on Tesla shares and rounding up one dollar because "he had recently learned about the number's significance in marijuana culture", and to impress his girlfriend, according to the SEC's complaint.