Lt. Col. David Lapan, a Marine Corps spokesman, said Cpl. Wassef Ali Hassoun would continue to undergo a "repatriation" process until it is determined he is fit and capable of returning to normal duty. He said the process could take from weeks to months.
Hassoun was not made available at Quantico for questions from reporters.
He left Ramstein Air Base in Germany on a morning flight aboard an Air Force C-5 Galaxy heavy transport plane and stopped first at Dover Air Force Base, Del., where he boarded an Air Force C-12 jet for the flight to Quantico.
A spokesman at Quantico, Marine Corps Capt. Jeff Landis, said Hassoun arrived at 3 p.m. EDT, and was received by a military support team that came from Hassoun's home base at Camp Lejeune, N.C.
The Navy has said it is investigating whether the kidnapping might have been a hoax, but the Naval Criminal Investigation Service is not expected to question Hassoun until his repatriation procedure is completed, the Marine Corps said.
As he departed the Landstuhl Regional Medical Center on Wednesday, Hassoun said he was anxious to get home.
"I am in good health and spirits, I look forward to my return home to friends and family," he said in a written statement provided to The Associated Press, his first public comment since he vanished June 20 from his base near the troubled Iraqi city of Fallujah.
Hassoun was flown to Germany Friday after reappearing July 8 at the U.S. Embassy in Beirut. It remains unclear how he made the journey to Lebanon from Iraq.
"All thanks and praises are due to God for my safety," he said. "I am also very thankful for all the kind wishes, support and praise for me and my family from my fellow Marines, all the people in the United States, Lebanon and around the world."
Hassoun signed the statement "Semper Fidelis," the Marine Corps motto meaning "always faithful."
During the three weeks he was missing, various conflicting reports emerged about Hassoun — first that he was kidnapped and beheaded, then that he was alive. There were suggestions it was all a hoax.
Hassoun's debriefing at Landstuhl was designed to help U.S. military specialists learn any lessons about the circumstances of his disappearance that could help others who find themselves in similar situations.