Dorsey has been under pressure to resign.
Twitter co-founder Jack Dorsey will be stepping down as Chief Executive Officer of the company.
CNBC cited anonymous sources familiar with the matter, while reporting the development.
Reuters and The New York Times have separately reported that they have been told the same.
Dorsey founded Twitter in 2006, and has been serving as Chief Executive of Twitter and payment firm Square.
BBC reports that Dorsey had been under pressure from some investors to step down last year, in favour of a CEO with a single focus.
Twitter’s share price jumped slightly as rumours of his departure emerged.
On Sunday, Dorsey had tweeted that: “I love Twitter.”
Dorsey is 45 years of age.
UPDATE: Dorsey has just announced on his Twitter page that he is resigning. “I want you all to know that this was my decision and I own it. It was a tough one for me, of course. I love this service and company,” he writes.
He adds that “there’s a lot of talk about the importance of a company being founder-led. Ultimately I believe that’s limiting and a single point of failure. I’ve worked hard to ensure that this company can break away from its founding and fathers.”
Parag Agrawal will succeed Dorsey as Twitter CEO.
Writer: Jude Egbas