Twitter Inc. is handing the chief executive reins back to Jack Dorsey, entrusting its founding architect to reassure investors and revive the social-media service’s sagging user growth. At the same time, Mr. Dorsey, 38 years old, will remain chief executive of Square Inc., the payments startup he co-founded after leaving Twitter in 2008.

By returning Twitter to its roots, the board is betting on its soft-spoken former leader to build a social-media powerhouse that can compete with Facebook Inc. for online advertising dollars and bring stability to a company that has been beset by frequent changes in the management ranks. Mr. Dorsey is credited with coming up with the initial idea for sharing status updates in 140 characters or less.

One of the largest investors in both Twitter and Square, Rizvi Traverse Management LLC, endorsed Mr. Dorsey’s dual CEO role.

Twitter employs 4,100 people and expects to generate more than $2 billion in revenue this year. But investors have grown restless with the service’s inability to resonate with average Internet users. Twitter claimed 316 million monthly active users as of June 30, but that number grew just 2.6% from the previous quarter.

The dual CEO club has only included a small group of tech executives, including his idol, Steve Jobs, who ran Apple Inc. and Pixar, and Elon Musk, founder of Tesla Motors Inc. and Space Exploration Technologies Corp.