The move comes with the one-to-many messaging platform struggling to boost its user base after a much-anticipated public offering in 2013.
Costolo guided the San Francisco-based firm through its initial public offering, but growth has been disappointing and the company has yet to show a profit.
A Twitter statement said Costolo would remain as a member of the Twitter board and that Dorsey would stay as CEO of Square, the financial technology group he founded, during the search for a new chief executive.
Twitter said it formed a committee that will work with “a leading executive search firm to assist in conducting a global search which will consider both internal and external candidates” for CEO.
Dorsey said in the statement: “The future belongs to Twitter thanks in large part to Dick Costolo’s dedication and vision.”
In its latest earnings report, in April, Twitter said it had a net loss in the quarter of $162.4 million.
The company said the number of active monthly users rose above 300 million, but that figure has been growing a pace too sluggish for many investors, and below rivals in social networking.