Last month Tesla and Musk were both fined $20 million over the tweets in which he claimed he was taking the company private at $420 a share, which the SEC alleges was a number chosen as a joke with his singer girlfriend, Grimes, who introduced him to marijuana.
Tesla announced that Elon Musk's replacement as its chair will be Robyn Denholm, now chief financial officer at Australian telecommunications operator Telstra.
Denholm, one of two female directors on the nine-member board, assumes her new position immediately, Tesla said.
The country's top financial markets watchdog had filed fraud charges against Mr Musk, ...
That deal required Musk to step aside as head of the board for three years in favor of an independent chairman.
The announcement scotches reports that James Murdoch was the frontrunner for the job.
Tesla has named a new chair to replace Elon Musk, after the CEO agreed to step down from the company's board as part of a settlement with the Securities and Exchange Commission. Tesla's shares soared following his comments.
She has only been CFO since October 1 this year, though she joined Telstra in January 2017 as its chief operations officer.
Tesla, which has never reported an annual profit, also came under strain over production schedules for its Model 3 electric auto, its newest vehicle aimed at a wider market.
Denholm will leave the Australian telco following a six-month notice period, during which her predecessor Elon Musk will provide her support to "ensure a smooth transition", according to the statement.
Besides Telstra, Denholm has worked in other tech companies such as Juniper Networks and Sun Microsystems, and she also worked for Toyota, the statement added.
A statement from Ms Denholm said she believed in Tesla and looked forward "to helping Elon and the Tesla team achieve sustainable profitability and drive long-term shareholder value".
Denholm has served on Tesla's board since 2014.