FoxNews.com automotive editor Gary Gastelu on Tesla's money troubles and Mike Manley, Fiat Chrysler's replacement for longtime CEO Sergio Marchionne.
Denholm had already served as a member of the Tesla board since 2014.
The SEC accused him of manipulating the market and sued him in late September for making "false and misleading" statements to investors.
Musk cited Denholm's long experience in the tech and auto industries as strong advantages and said in a statement that he looked forward to working with her.
"So that she will be able to devote her full attention to the Tesla chair role, Robyn will be leaving her role as CFO and head of strategy at Telstra. once her six-month notice period with Telstra is complete", the carmaker said.
The spokeswoman added that Tesla was actively looking for two additional independent directors.
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Tesla announced that Elon Musk's replacement as its chair will be Robyn Denholm, now chief financial officer at Australian telecommunications operator Telstra.
The settlement required Tesla and Mr Musk to pay a fine of $20 million each and for Mr Musk to give up his chairman role for three years.
"The fact that he can remain CEO is very important for the company".
Tesla has seen months of turbulence since Musk's infamous tweet.
The 55-year-old Australian will temporarily step down as chair of Tesla's audit committee until she quits Telstra.
Aside from her work at Telstra, she has also spent time at technology majors including Juniper Networks and Sun Microsystems.
"To ensure a smooth transition during the remainder of Robyn's time at Telstra, Elon will be a resource to Robyn and provide any support that she requests in her role as Chair", Tesla said in a news release. Musk later tweeted that this was "incorrect".