When he finds someone foolish enough to take the job, Musk will step down as CEO.
A majority of users voted "yes" to him quitting the role in a poll on the social networking site.
After his replacement is found, he will continue to run the software and server teams.
The changes on the platform have been criticized.
The BBC is not responsible for the content of external sites.View original tweet on TwitterI will resign as CEO as soon as I find someone foolish enough to take the job! After that, I will just run the software & servers teams.
— Elon Musk (@elonmusk) December 21, 2022
Since buying the site, Mr Musk has fired half of it's staff and tried to roll out a paid-for verification feature, but put it on hold. Last week, the feature was re-launched.
Civil liberties groups accuse him of taking steps that will increase hate speech.
The UN said that media freedom was not a toy.
This is the first time the billionaire has responded to a question about his future. More than 17 million users voted on the matter.
Mr Musk said it may be difficult to find someone to take over the social media platform. Bankruptcy is not out of the question after the billionaire told the remaining workers that the company he just bought could see a negative cash flow in the next five years.
Following this week's poll, he said "no one wants the job who can actually keepTwitter alive."
Jack Dorsey could return to run the company, according to some people. He stepped down as chief executive.
Other names mentioned as possible replacements include Sriram Krishnan, engineer and close aide to Mr Musk, and the son-in-law of the president.
Mr Musk has obeyed polls before. "The voice of the people is the voice of God" is a phrase he likes to quote.
He said that paid subscribers would only be allowed to vote on changes to policy in the future.
One user claimed that so-called bots voted heavily in the poll about Mr Musk's role at the firm. Mr Musk was intrigued by the claim.
It certainly wasn't nice for Musk to stay at the helm of the micro-blogging site.
It felt like a train was coming off the tracks.
He liked the circus he made. Did he get bored, did his investors pull him back, or did he finally listen to those who told him that the CEO of the electric car firm that links much of his wealth is in dire straits?
Perhaps one day Mr Musk will let us know how open he is on social media.
The Musk show is not over. He will still own the firm, even though nobody is likely to buy it off him anytime soon, and he will still be a prolific and influential tweeter.
He needs to find someone willing to take his place and work with him, and that position might be hard to fill.
After it was paused, the paid-for verification feature was rolled out again last week. The service costs $8 per month, or $11 for people who use theTwitter app on Apple devices, and gives subscribers a blue tick.
A blue tick used to be free, but now it's a Badge of authenticity.
For weeks, investors have been calling on Mr Musk to step down from running the social media platform, saying he has been distracted from running the company.
The company's shares have plummeted over the last year.
The shares were pushed down by Mr Musk's sale of billions of dollars worth of shares.
"This is finally a good step in the right direction to end this painful nightmare situation for investors in the company," said Dan Ives from investment firm.