The move is effective immediately, Twitter said in a statement, but Mr Dorsey will remain on the board until his term expires in 2022.
“I’ve decided to leave Twitter because I believe the company is ready to move on from its founders,” Mr Dorsey said in the statement.
“My trust in Parag as Twitter’s CEO is deep. His work over the past 10 years has been transformational. I’m deeply grateful for his skill, heart and soul. It’s his time to lead.”
In a personal statement to Twitter employees, Mr Dorsey added that the decision to leave Twitter was “tough".
“I'm really sad … yet really happy,” he wrote. “There aren't many founders that choose their company over their own ego. I know we'll prove this was the right move.”
Twitter's stock price surged more than 10 per cent in premarket trading after CNBC first reported news of the move. Gains were quickly pared before trading in the stock was halted for about an hour before Twitter's confirmation of Mr Dorsey's departure.
In 2020, Mr Dorsey came under pressure from activist investor Elliott Management over how he was spending his time.
A year earlier, he had also said he planned to spend up to six months of the year working in Africa to better understand the continent’s internet users, a move that was ultimately scrapped due to Covid-19.
The hedge fund reached an agreement with Twitter and private equity group Silver Lake to appoint three new directors to Twitter’s board and create a committee to review its leadership and governance. Mr Agrawal, who became chief technology officer in 2017, will become a member of the board.
Mr Dorsey also oversaw the company when it faced widespread pressure from politicians and activists to take a more proactive role in moderating hate speech, misinformation and other forms of objectionable content from political leaders.
He took a stronger line than his social media peers during Donald Trump’s presidency, banning the former president from Twitter and telling Congress that he takes some responsibility for online organising that led to the January 6 riot at Capitol Hill. The company also recently introduced a programme to crowdsource fact-checking misinformation.
Mr Dorsey helmed Twitter as it experimented with new innovations in social media including most recently live audio products and subscription services.
In June, the company unveiled Twitter Blue, a long-awaited subscription service that will allow users to rescind tweets and organise their posts. It also launched Twitter Spaces, a live audio chat service that were meant to compete with upstart Clubhouse.
Twitter's stock price is down about 10 per cent so far this year.
Agencies contributed to this report.