The move is meant to usher Tesla past months of turbulence following Musk's Aug. 7 tweet that he was considering taking the company private and had secured funding.
The fallout, which included the US Securities and Exchange Commission subsequently filing fraud charges against Musk for what it said were his "false and misleading" tweets, led some investors to call for stronger board oversight of Musk.
The inclusion of Ellison puts one of the world's richest people with experience building a startup into a successful company on Tesla's board. He served as a director at Apple
Joining Ellison on the board, effective Dec. 27, was Walgreens Boots Alliance's
Charles Elson, director of the corporate governance centre at the University of Delaware, questioned adding a friend of Musk's and another director with no experience at an industrial company like Tesla.
"Why would you put a friend (on the board) if the idea of the two independent directors were to be objective," Elson said. "Investors who were hoping for two newly objective directors who could stand up to Mr. Musk would be rather disappointed by the choice."
Under a court-approved agreement with the SEC, Musk agreed to pay a $20 million fine and step aside as Tesla's chairman for three years to settle charges that could have forced his exit. Tesla also agreed to name the independent directors and a board committee to control Musk's communications.
SEC officials could not be reached to comment on Friday, but Harvey Pitt, the agency's former chairman, called the addition of Ellison a positive step.
"His personal investment in Tesla stock - said to be his largest personal investment outside of Oracle - means he will be focused on ensuring that Tesla develops profitable strategies," Pitt said. "He also has the stature to stand up to Mr. Musk, should that become necessary."
Tigress Financial Partners analyst Ivan Feinseth said Ellison's "maverick type CEO traits" match Musk's.
Ellison bought 3 million shares of Tesla earlier this year. Through a spokeswoman, he declined to comment.
Tesla's shares closed up 5.6 per cent at $333.87 on Friday.
Musk on Friday afternoon tweeted his welcome: "Excited to have Larry Ellison & Kathleen Wilson-Thompson join the Tesla board!"
In November, Tesla named director Robyn Denholm as board chair, fulfilling one of the SEC's demands. Denholm, who joined Tesla as an independent director in 2014 and agreed to step down as finance chief of Australian telecoms firm Telstra Corp Ltd
Tesla said it conducted a "thorough, expansive" search process for the directors, calling Ellison a "preeminent entrepreneur" and Wilson-Thompson "a human resources leader" and said both had a passion for sustainable energy. They bring the Tesla board count to 11 people.
The larger-than-life Ellison, like Musk, is known for making bombastic, brash public comments. He went on a diatribe attacking cloud computing at a 2008 analyst conference, which only served to highlight Oracle's slow move into the space. He undermined Oracle's business relationship with Hewlett Packard in 2010 in an email to the New York Times that chastised the board for firing its CEO and his friend, Mark Hurd, after a sexual harassment inquiry.
He rarely interacts with journalists or blogs, and has only tweeted once - a 2012 message promoting Oracle's cloud products.
"VERY CLOSE FRIENDS"
Ellison, said by Forbes magazine to be worth $55 billion, has in the past defended Musk.
"I'm very close friends with Elon Musk, and I'm a big investor in Tesla," Ellison, 74, said on a Oct. 26 conference call with analysts.
"This guy is landing rockets," Ellison added about Musk, referring to his leadership of SpaceX. "He's landing rockets on robot drone rafts in the ocean, and you're saying he doesn't know what he's doing. Well, who else is landing a rocket?"
Wilson-Thompson, who could not be immediately reached for comment, spent 17 years at Kellogg Co
Musk has gained fans for his bold approach to business and technology, using his almost 24 million Twitter followers to promote Tesla, SpaceX and tunnel venture Boring Co.
But the August claim that he had the funding to take Tesla private, and a subsequent U-turn, stunned Wall Street. It all came as Musk was filmed briefly smoking marijuana during a live Web show and as he called a British diver in the Thai cave rescue a "pedo."
Tesla's market cap exceeds that of traditional, established U.S. automakers that make millions of vehicles and billions of dollars in profits annually, and the company has garnered legions of fans despite repeated production issues.
(Additional reporting by Jim Finkle, Katanga Johnson and Akanksha Rana; Editing by Sriraj Kalluvila, Steve Orlofsky and Tom Brown)