Dorsey cited three reasons for his departure, two being the appointments of Agrawal and chairman Bret Taylor, which he both supported. The third reason cited was the Twitter team. "We have a lot of ambition and potential on this team."
Dorsey added: "I want you all to know that this is my decision and I own it."
Shares of Twitter surged on earlier reports that Dorsey would be stepping down.
Twitter's stock, which has consistently underperformed the market, jumped more than 10 per cent at the opening bell Monday before trading was halted pending news.
CNBC first reported that Dorsey may step down soon, citing anonymous sources.
Twitter Inc. did not immediately respond to a request for comment from The Associated Press early Monday. On Sunday, Dorsey sent the tweet "I love Twitter."
Dorsey is also the top executive at Square, a financial payments company that he founded, and some big investors have openly questioned whether he can be effective leading both.
Last year, the company came to an agreement with two of those activist investors that kept Dorsey in the top job and gave a seat on the company board to Elliott Management Corp., which owned about 4 per cent of Twitter's stock, and another to Silver Lake.
Twitter was caught up in the heated political atmosphere leading up to the 2020 election. Former President Donald Trump was banned from Twitter, with Dorsey defending the move, saying the January 6 Capitol riot and Trump's tweets after the event resulted in a risk to public safety and created an "extraordinary and untenable circumstance" for the company.
Trump sued the company, along with Facebook and YouTube, in July for alleged censorship.
The early days of Twitter began with a tweet sent by Dorsey on March 21, 2006, that read "just setting up my twttr". Twitter went through a period of robust growth during its start, but as the growth slowed the San Francisco company began tweaking its format in a bid to make it easier and more engaging to use.
Dorsey initially became Twitter CEO in 2007, but was forced out the next year. He returned to the role in 2015. - AP