BOSTON—General Electric Co. has agreed to sell its industrial gas-engine business to Advent International for $3.25 billion, according to CEO John Flannery said Monday that the private-equity firm will acquire GE’s Jenbacher and Waukesha engine brands and manufacturing sites in Austria, the U.S. and Canada. The deal is expected to close in the fourth quarter.

Distributed Power produces heavy-duty engines that generate power and heat for industrial facilities. The business, which has about 3,000 employees, posted sales of $1.3 billion last year. Its sale furthers Flannery’s pledge to narrow GE’s focus as he seeks to stem one of the deepest slides in the company’s 126-year history. The CEO agreed last month to unload GE’s locomotive division as part of an effort to sell $20 billion of assets.

The on-site turbines are also used on college campuses as a way to keep buildings running when the grid goes dark. Increasingly, small gas turbines are seen as the backbone of microgrids that are reshaping the way communities get power because they can back up supplies from solar panels or battery systems.

GE has owned Jenbacher, named for the Austrian town Jenbach, since 2003. Seven years later, the company added Waukesha, which takes its name from a city in Wisconsin, through the acquisition of Dresser.