In a tweet on Monday, Jack Dorsey, 45, who co-founded the business in 2006, announced his departure.
"because I believe the company is ready to move on from its founders..... finally time for me to depart,"
Parag Agrawal, the microblogging site's previous Chief Technology Officer, has been named the new CEO.
Agrawal thanked Dorsey and the Twitter team for selecting him in a tweet.
“Deep gratitude for @jack and our entire team, and so much excitement for the future. Here’s the note I sent to the company. Thank you all for your trust and support.”
Twitter's stock soared after the news that Dorsey would step down, according to Sky News.
On Monday morning, shares of the social media platform soared 9% on the start of the market.
After the rise, trading on the New York Stock Exchange was paused, but shares resumed trading with a gain of more than 4.5 percent ahead of the opening price.
Dorsey is still the CEO of Square, a financial payments company with a market capitalization of nearly $98 billion (£73 billion), compared to Twitter's $38 billion (£28 billion).