Rosengren has run Sandvik since November 2015, overseeing implementation of a decentralised structure to help make it more efficient and flexible. He will become ABB CEO in February next year, replacing Peter Voser.
Prior to his Sandvik time Rosengren ran Wartsila Corporation, which makes power systems for the marine and power generation markets.
Voser, also ABB chairman, said Rosengren would bring the managerial skills ABB needed for the next stage of its transformation.
"He understands how to establish successful decentralised organisations, empower people and demonstrates the culture of cooperation and high performance," Voser said.
Rosengren said he looked forward to the job ahead at ABB.
"At such a pivotal time for manufacturing industries, ABB must continue to best serve the needs of global customers with a unique technology and digital solutions portfolio to help enhance their productivity," he said.
Sandvik chairman Johan Molin said the company would embark on the hunt for a new CEO.
"Bjorn Rosengren has, since he joined Sandvik in November 2015, established a solid decentralised business model for the company and made the organisation more flexible and efficient," Molin said.