Musk, who took over as owner of the social media platform last year, did not reveal the identity of his replacement, apart from saying she will be "starting in 6 weeks".
In the meantime, his role will "transition to being exec chair & CTO, overseeing product, software & sysops," her wrote in a Twitter post on Thursday.
The billionaire entrepreneur, 51, has said in recent months he had been planning to find a new CEO for the San Francisco-based company.
In November 2022, just a few weeks after buying Twitter for $44 billion (£35 billion), he told a US court that he does not want to be the CEO of any company.
While testifying, Musk said: "I expect to reduce my time at Twitter and find somebody else to run Twitter over time."
He later tweeted: "I will resign as CEO as soon as I find someone foolish enough to take the job."
The pledge came after millions of Twitter users asked him to step down in a poll on the platform Musk himself created and promised to abide by.
Shares of Tesla - the electric car company which Musk owns - rose about 2% on Thursday after he made the announcement.
Last November, he was questioned in court about how he splits his time among Tesla and his other companies, including SpaceX and Twitter.
Musk said he never intended to be CEO of Tesla, and that he did not want to be chief executive of any other companies either, preferring to see himself as an engineer.
Musk's time as Twitter CEO has triggered periods of criticism, including his decision to sack more than half of the workforce he originally inherited.
He has also introduced a paid-subscription verification process for Twitter users, ending the blue check system in favour of new product 'Twitter Blue,' and reactivated the accounts of figures who had previously been suspended, including former US president Donald Trump.
Want a quick and expert briefing on the biggest news stories? Listen to our latest podcasts to find out What You Need To Know...