Musk was named to join the Twitter board after buying a major stake in the firm and becoming its largest shareholder.
"Elon has decided not to join our board," Twitter CEO Parag Agrawal tweeted.
"Elon's appointment to the board was to become officially effective 4/9, but Elon shared that same morning he will no longer be joining the board," Agrawal said.
"I believe this is for the best."
Currently the world's richest man and with more than 80 million followers on the microblogging platform, Musk last week disclosed a purchase of 73.5 million shares -- or 9.2 percent -- of Twitter's common stock.
Agrawal had announced on Tuesday that Musk would be joining the board, describing him as "a passionate believer and intense critic of the service which is exactly what we need".
Musk himself tweeted that he was "Looking forward to working with Parag & Twitter board to make significant improvements to Twitter in coming months!"
In his announcement Sunday, Agrawal shared a note he sent to Twitter, which said Musk's appointment to the board would be contingent on a background check and that he would have to act in the best interests of the company once appointed.
"Elon is our biggest shareholder and we will remain open to his input," Agrawal added.
