Mr DeSantis was re-elected with nearly 60% of the vote in the midterms and has been tipped as a potential candidate to be the next US leader.
Musk’s apparent endorsement of Mr DeSantis comes as rival Republican Donald Trump has been under fire for dining with a known white supremacist.
Asked if he would support DeSantis in 2024, the Tesla owner replied in a tweet: “Yes.”
“As a reminder, I was a significant supporter of the Obama-Biden presidency and (reluctantly) voted for Biden over Trump,” Musk said.
When asked previously about Musk’s support, Mr DeSantis joked: “I welcome support from African-Americans, what can I say.”
Musk, who is white, grew up in South Africa.
Mr Trump distanced himself on Friday from a pre-Thanksgiving dinner at his Mar-a-Lago club in Florida with rapper Kanye West and white supremacist Nick Fuentes.
He has claimed he didn’t know the identity of the far-right activist who was unexpectedly brought along with the rapper, NBC reports.
In a statement on his Truth social platform, Mr Trump said: “This past week, Kanye West called me to have dinner at Mar-a-Lago. Shortly thereafter, he unexpectedly showed up with three of his friends, whom I knew nothing about.”
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