He served as the interim boss of the company for three months after Dick Costolo stepped down on 1 July.
Mr Dorsey will remain the head of mobile payments company Square, but will step down as chairman of Twitter.
Mr Costolo, who was chief executive from 2010 to this year, had been under pressure from investors unhappy with the firm’s user growth.
Twitter had previously said the chief executive job would be a full-time position, which seemed to exclude Mr Dorsey as long as he continued to run Square.
Twitter listed its shares on the New York Stock Exchange in 2013, but under Mr Costolo the social network had not been adding users as fast as investors had hoped.
In April, the firm missed Wall Street’s forecasts for revenue growth and reported a net loss of $162m (£104m).
Its share price has declined nearly 50% since then.
This will be Mr Dorsey’s second stint as Twitter chief executive, having held the position between May 2007 and October 2008.
In addition to his positions at Twitter and Square, he will also stay on as a member of the Disney board.