Agrawal, a 10-year Twitter veteran, is part of a board strategy to double its annual revenue by 2023. Dorsey, who co-founded Twitter in 2006, is leaving after overseeing the launch of new ways to create content through newsletters or audio conversations while simultaneously serving as CEO of his payments processing company Square.
His job has been somewhat of a poisoned chalice as he had to deal with US President Donald Trump's administration before banning the Republican from the platform after he used the platform to support his failed coup.
Dorsey will remain on the board until his term expires at the 2022 annual shareholder meeting, the company said.
Dorsey hinted of a boardroom coup saying he chose to step down “due to the strength of Agrawal's leadership” which was a rather odd thing to say.
"I'm really sad ... yet really happy.There aren't many companies that get to this level", adding that his move to step down "was my decision and I own it".
Agrawal said in an email to employees: "We recently updated our strategy to hit ambitious goals, and I believe that strategy to be bold and right. But our critical challenge is how we work to execute against it and deliver results."
Over the past year, Twitter has fought to end years-long criticism that it has been slow to introduce new features for its 211 million daily users and was losing ground to social media rivals like Instagram and TikTok.
Under Dorsey's leadership, Twitter acquired email newsletter service Revue and launched Spaces, a feature that lets users host or listen to live audio conversations.
The company also rolled out advertising improvements to help brands find Twitter users likely to be interested in their product, a key component of the company's goal to double annual revenue by 2023.
Twitter shares have slumped in recent months, adding pressure on Dorsey to end his unusual arrangement of being CEO of two public companies.
In early 2020, Dorsey faced calls from Elliott Management Corp to step down, after the hedge fund argued that he was paying too little attention to Twitter while running Square.