The Senate approved her appointment to the command at Wright-Patterson Air Force Base in Ohio late Monday, the Dayton (Ohio) Daily News reported.
Since September, Wolfenbarger has been working in the Pentagon. From December 2009 to September 2011, she was vice commander at Wright-Patterson.
An Ohio native, Wolfenbarger graduated from the Air Force Academy in 1980 in the first class to include women.
"The men and women of the U.S. Air Force have relied on the experience and courage of General Wolfenbarger," U.S. Sen. Sherrod Brown, D-Ohio, said. "With roots in the Miami Valley, she has shown strong leadership and an eagerness to serve throughout her career. I'm humbled to congratulate General Wolfenbarger for this well-deserved promotion and proud that the Air Force's first female four-star general was born in Ohio, raised in Ohio, and will serve in Ohio as the commander of the Air Force Materiel Command in Ohio."
Gen. Ann Dunwoody, head of U.S. Army Materiel Command, became the first woman in the military to be a four-star general when she was named to the position in 2008.