The privately held company announced the change in command Monday.
Costolo, an early investor in Twitter, joined the company as chief operating officer a year ago to help manage Twitter's rapid growth.
Since then, Twitter has moved into a larger headquarters in San Francisco as its payroll swelled from a few dozen workers to 300 employees.
Twitter launched in 2006. Williams became CEO in 2008, after Twitter's board decided he was better equipped for job than another co-founder, Jack Dorsey.
Williams will remain at Twitter and focus on developing new products.