Singh is currently chairman of Docker's board, and will continue in that role. Singh was previously CEO of expenses management software company Concur, which was acquired by SAP in 2014; he then became an executive board member at SAP.
Ben Golub, Singh's predecessor as CEO of Docker, will stay on as a director on Docker's board.
"Steve brings over 20 years of experience in building and scaling world-class software companies including some of the most successful brands in technology," Docker said.
By automating the creation and deployment of apps in containers -- a lightweight form of virtualisation -- Docker's software aims to reduce costs for developers and streamline processes so that they can ship new features faster.
Docker said it's seeing "strong momentum" in the enterprise software market, with hundreds of commercial customers including ADP, GE, Visa and MetLife. The company said there are now over 900,000 "dockerized" apps, which have been downloaded over 13 billion times.
"Over the past four years, Docker has grown at an incredible rate. We are now seeing widespread traction in the developer community and the enterprise market," said Solomon Hykes, Docker's founder and CTO.