Dorsey will remain on the board until at least 2022, the company said, with Bret Taylor becoming independent chairman. Agrawal, Twitter's current chief technology officer since 2017, will assume CEO duties immediately.
Agrawal is slated to speak at a Barclays investor event on December 7, alongside current CFO Ned Segal.
Dorsey, 36, co-founded Twitter in 2006 but was forced out as CEO two years later. He was brought back in 2015, however, in a effort to re-boot growth -- and tackle online abuse -- amid the social media group's growing global influence.
"I've decided to leave Twitter because I believe the company is ready to move on from its founders," Dorsey said. "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."
"I want you to know that this was my decision and I own it," he added in a statement posted on his verified Twitter account.
Twitter shares were marked 0.3% lower in early afternoon trading, after being halted by officials on the Nasdaq, to change hands at $46.87 each.
Activist investors Elliot Management, in fact, pushed for change at the top of the group in early 2020, before cutting a deal later in the year that included a $1 billion investment from Silver Lake and a pledge to "evaluate the CEO succession plan" with Dorsey and "and make recommendations consistent with corporate governance best practices with respect to the elimination of the Company's staggered board."
"Twitter is now executing against an ambitious multi-year plan to dramatically increase the company's reach and value, and we look forward to the next chapter of Twitter's story," Elliott said in statement Monday. "Having gotten to know both incoming Chairman Bret Taylor and incoming CEO Parag Agrawal, we are confident that they are the right leaders for Twitter at this pivotal moment for the company."
Last month, Twitter posted stronger-than-expected quarterly revenue growth of 37%, taking its ad sales to $1.14 billion, as the group appeared to avoid the worst of the impact of privacy changes in Apple Inc.'s AAPL new iOS update.
Monetizable active users, however, were pegged at 211 million for the quarter, just shy of analysts' forecast of 212.6 million, with much of the growth coming from outside the United States.
Looking into the final months of the year, Twitter said it sees revenues in the region of $1.56 billion to $1.6 billion.