He will lead operations in more than 100 markets in Africa, Asia Pacific and the Middle East.
"Stefan is a great addition to an already strong team," CEO Dan Akerson said in a statement. "We expect him to continue building on his record of delivering results in markets around the world."
Jacoby will report to Akerson and begin on Aug. 5.
Lee moves to the China role after nearly four years in charge of the international unit. He will remain head of global manufacturing, GM Bob Socia, president of GM China, will continue to report to Lee.
"GM leads in the U.S. and China, the two most important auto markets in the world," Akerson said. "We are also in the midst of the most aggressive product rollout in our history. Tim is critical to building on our success in China and to ensuring flawless vehicle launches around the globe."
Jacoby said GM's customer focus and momentum are two reasons he is joining the automaker. "The GM team has plans to win in every market, and I'm eager to contribute," he said in the statement.