Musk resigned as Tesla chairman in October under an arrangement with United States regulators to settle fraud charges stemming from a tweet in which he said he planned to take the company private and had financing to do it.
Tesla has appointed Robyn Denholm as chair of its board, replacing the electric carmaker's billionaire founder Elon Musk.
Robyn Denholm, Telstra's chief financial officer and head of strategy, has been named to head the company's board with immediate effect late Wednesday, the automaker said in a statement posted to its blog.
Telstra said she would be leaving her CFO role in the coming months.
Musk said: "Robyn has extensive experience in both the tech and auto industries, and she has made significant contributions as a Tesla board member over the past four years in helping us become a profitable company".More news: Ariana Grande named 2018 Billboard Woman of the Year
Musk's successor, effective immediately, will be Robyn Denholm, a former Tesla board member and technology executive. "Great respect. Very much look forward to working together", Musk tweeted early on Thursday. The 47-year-old billionaire will remain as chief executive.
The tweets sent shares in Tesla soaring to a high of $387.46 a share on August 7.
"The market reacted to this information and Tesla's stock price quickly traded up", said Stephanie Avakian, the SEC's Co-Director of the Division of Enforcement, in a September news conference.
Investors had also called for stronger oversight of Mr Musk after his erratic behaviour attracted attention.
The tech whiz Musk is also facing legal action from British diver Vernon Unsworth, who helped to rescue a football team of Thai boys when they became trapped in a cave, by falsely accusing him on Twitter of being a pedophile. In media interviews he said he often slept on a sofa in the Tesla office and more recently in an online video he briefly smoked marijuana.