Mr. Norwood's colleagues in Congress pushed the bill as a tribute to the former combat dentist who made Augusta his home after returning from the Vietnam War.
Mr. Norwood died in February at age 65 after suffering from lung disease and cancer. He had just begun his seventh term in Congress, where he was known for his efforts to win funding for veterans' health care and to pass a "patients' bill of rights" aimed at giving consumers better access to care.
"This is an extremely fitting tribute, because those of us who served in the Congress with Charlie over the years know firsthand how dedicated he was to our veterans and to meeting their needs," said Sen. Saxby Chambliss, of Moultrie.
Renaming of VA hospitals is somewhat rare.
The agency has nearly 160 medical centers nationwide, and only about 30 of them are named after people, according to a spokesman.
Of Georgia's three centers, in Augusta, Dublin and outside Atlanta, only the Dublin facility has been renamed -- after former Rep. Carl Vinson of Milledgeville, who served in Congress from 1914 to 1965.
A captain in the Vietnam War, Mr. Norwood was a member of the Army's dental corps and helped develop operating procedures for combat treatment that are still in use today. He earned the Combat Medical Badge and two Bronze Stars.
The bill approved Thursday passed the House and Senate earlier this year without opposition.
It was sponsored by Georgia's entire congressional delegation save for Rep. Jim Marshall, a Macon Democrat. Mr. Marshall did not oppose the measure but said he didn't sign on as a sponsor because he generally believes such honors should be reserved for military heroes or fallen soldiers.