While Amber got divorced from Johnny Depp in January after filing a case of physical violence against him in May a year ago, Elon has been married twice before.
There were reports about the two being in a relationship but it is only recently that they came out to the public, per Daily News.
Heard's short-lived marriage to actor Johnny Depp ended after their divorce was settled in August 2016, with Heard receiving $US7 million.
The new lovers spent time together this weekend in Australia, where Amber has been filming her new movie "Aquaman".
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Musk, the high-profile billionaire who founded Hawthorne-based SpaceX and owns Tesla electric auto company, broke with his tradition of mostly just sharing work-related photos on his Instagram account, showing a photo of Heard's arm draped over his shoulder. He also wrote that he and Heard had a great time with team of "Aquaman".
Rumors about Heard and Musk dating have been circulating since January, but the couple repeatedly insisted that they were "just friends". Now, the couple finally provided a confirmation of their relationship, according to E!
Elon Musk is the founder of Tesla, which is a world leader in electric cars, and SpaceX, which is pioneering space flight. He has five children from his first marriage with Justine Wilson, and divorced British actor Talulah Riley for the second time previous year. Remarried again in 2013.
"The bared armpit is a signal of confidence and status and the very open laughter suggests she's a different woman from the one adopting cooler and more serious poses with her ex".