His nomination had been placed on hold by Sen. John Cornyn, R-Tex, due to concerns over sexual abuse incidents at Joint Base San Antonio-Lackland, Texas.
Cornyn lifted the hold Aug. 2 following a meeting with Welsh.
"It's clear that Gen. Welsh shares my grave concerns," Cornyn is quoted by an Air Force Association account. "I am pleased to hear that he will follow the investigation wherever it may lead."
Welsh will assumed the Air Force's top post when the current chief, Gen. Norton Schwartz, retires Aug. 10.
"I fully accept the responsibility to stand beside Secretary of the Air Force Michael Donley and lead the 690,000 active, Guard, Reserve and civilian airmen who successfully serve our nation," Welsh is quoted in a Pentagon news release.
Welsh comes to the new job after serving as commander of U.S. Air Forces in Europe. He entered the Air Force in June 1976 after graduating from the Air Force Academy. The fighter pilot has held numerous operation, command and staff positions during his career.