Musk agreed to an independent chairman being appointed as part of a settlement with USA regulators that allowed him to remain chief executive.
Musk was forced to give up the role as part of a settlement with the Securities and Exchange Commission over a lawsuit filed against him for his infamous "funding secured" tweet made in August in regards to taking Tesla private, though he remains CEO of the electric vehicle manufacturer.
The settlement requires Tesla to install an independent chairman, among other penalties.
The task is not entirely new for Denholm; she's served on the Tesla Board as an independent director since 2014.
But upon taking her new role as chairwoman of Tesla, Denholm will step down from her CFO role at Telstra once her six-month notice completes.
An Australian accountant, Denholm is now finance chief at telecoms firm Telstra Corp Ltd and replaces Musk after he was forced to relinquish the role as part of a deal to head off charges of fraud by the Securities and Exchange Commission.
The settlement required Tesla and Musk to pay a fine of $20 million each and for Musk to give up his chairman role for three years. She also has worked at various technology companies including Juniper Networks and Sun Microsystems and held finance management posts at Toyota Motor Corp.in Australia.
"She's from Musk's inner circle and is unlikely to put obstacles in the way of decisions", Schwope said.
In premarket trade on the Nasdaq exchange Thursday, Tesla's share price was up 0.24 percent at $349.00. A spokesperson at the company told CNBC that Denholm will receive 8,000 stock options each year and a cash retainer of $300,000 once she leaves Telstra.
The billionaire later said he was not 'on weed' when he posted a tweet which said Tesla would be taken public with shares priced at $420 - a number which refers to a day in April when hordes of skunk-hounds congregate in parks and town squares to openly smoke cannabis. The aim is to provide stronger oversight to match Tesla's growing stature and market value. The money will go to shareholders who lost money following Musk's tweet.