He announced the news on the social media platform, which he bought last year for $44bn (£35.2bn).
Mr Musk has been under pressure to name someone else to lead the company and focus on his other mega businesses.

Last year, after Twitter users voted for him to step down in an online poll, he said: "No one wants the job who can actually keep Twitter alive."

However, although the eccentric billionaire had said he would hand over the reins, it was by no means clear when or even if it would happen.
Tesla shares jumped after the announcement. Mr Musk has previously been accused by shareholders of abandoning Tesla after his takeover of Twitter and damaging the car company's brand.

It is sometimes difficult to know when the billionaire and owner of Twitter is being serious.

Last month, when the BBC asked Mr Musk who was going to be boss of Twitter, he said he had made a dog Twitter's leader.

But if Elon Musk has indeed appointed a female chief executive, it would be a major departure from the typical tech boss.

The vast majority of leaders of major tech companies are men.

Although Mr Musk has talked about paid subscribers to Twitter Blue, it's advertising that brings in the vast majority of revenue at Twitter.

The new boss will no doubt seek to improve relationships with advertisers, and smooth their fears over content moderation.

Mr Musk, a self-proclaimed free speech absolutist, has said he took over Twitter to protect free speech. However advertisers do not want their content next to misinformation or extremist content.

Mr Musk purchased Twitter in October only after a lawsuit forced him to go through with the deal. Upon taking charge, Mr Musk controversially fired thousands of staff in a bid to cut costs at the firm, which has struggled to be profitable.

In March, the billionaire said those efforts had paid off and the platform's finances were improving.

And last month he told the BBC that most of the advertisers that had abandoned Twitter immediately after the acquisition had returned.