Major General Kenneth Dahl, who served in combat in Afghanistan, has been appointed to lead the investigation.
Sgt. Bowe Bergdahl, 28, returned to the US after five years in captivity on Friday.
Shortly after his release, several commentators and soldiers came forward to brand him a deserter and call for him to be punished.
The Pentagon has previously concluded Sgt. Bowe Bergdahl walked off base in Paktika province without authorization, but officials have not determined whether he intended to desert.
Bowe Bergdahl was flown from a military hospital in Germany to Brooke Army Medical Center in Texas on Friday, where he will complete the final phase of the reintegration process.
He was released by the Taliban in late May in exchange for five Guantanamo Bay detainees, a move that has been criticized by some lawmakers.
In a statement, the defense department said Maj. Gen. Kenneth Dahl would have access to evidence gathered in 2009 shortly after Sgt. Bowe Bergdahl was captured.
But officials will not be able to interview him until a team working on his “reintegration” will allow it.
“We ask that everyone respect the time and privacy necessary to accomplish the objectives of the last phase of reintegration,” the department said in a statement, adding there is no timeline for wrapping up the investigation.
On Friday, Maj. Gen. Joseph DiSalvo said Bowe Bergdahl “looked good” as he returned to Texas and was in uniform and saluted.
Sgt. Bowe Bergdahl had not yet been in contact with his family, which officials described as his own choice.
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