In July this year, the then CEO Dick Costolo had stepped down from his position and Dorsey was appointed as the interim CEO as the Board scouted for a new head.
Dorsey had earlier served as Twitter's President and CEO from May 2007 to October 2008.
"On September 30, 2015, the Board of Directors of Twitter, Inc. Appointed Jack Dorsey, co-Founder and interim CEO, as CEO. Mr Dorsey will continue to serve as a member of the Board, but will no longer act as Chairman," Twitter said in a statement.
The Board has also appointed Adam Bain as the Chief Operating Officer.
Also Read
Bain, 42, served as Twitter's President, Global Revenue and Partnerships from September 2010 to October 2015. Previously, he has worked with News Corporation and Fox Audience Network.
The statement said Dorsey will continue to serve as CEO of Square, Inc., the payments and financial services company, he co-founded in 2009.
Currently, he also serves on the boards of The Walt Disney Company and Square, Inc.
"Mr Dorsey was selected to serve on the Board because of the perspective and experience he brings as one of Twitter's founders and as one of Twitter's largest stockholders, as well as his extensive experience with technology companies," the statement said.
Costolo described Dorsey (@jack) as a calm and thoughtful leader. "He is bold, forthright, decisive, and the team loves working with him," he wrote in a tweet.
In another tweet, he wrote: "as I step off the board, two reminders: those banging pots and pans outside Twitter know the least about what's going on inside Twitter and there is only one narrative that matters and it's the one you'll create for the world".
Globally, Twitter has 316 million users as of June 2015.
Recently, Instagram (which is owned by Facebook) announced it has 400 million monthly active users, ahead of Twitter. Facebook has 1.49 billion monthly active users.