A defense official, speaking on condition of anonymity, said the general had been appointed to conduct the army investigation of Sergeant Bergdahl's June 2009 disappearance and capture, but said the probe had not yet begun.
The official declined to name the general.
Bergdahl, who was released on May 31 in a prisoner exchange with the Taliban, arrived at a military hospital in Texas on Friday.
While the release of Bergdahl, who had been the only U.S. prisoner of war, was widely hailed initially, it has also attracted widespread criticism, in part from lawmakers who say the five senior Taliban figures freed from the Guantanamo Bay prison in exchange for Bergdahl could return to the fight.
Lawmakers have also complained that the Obama administration failed to give Congress required 30-day notice before releasing the Taliban to Qatar.
Some of Bergdahl's former peers in Afghanistan have alleged the soldier, now 28, walked away from his post voluntarily. But the Pentagon has said the circumstances of his disappearance and capture were unclear.
An earlier U.S. military investigation found he had slipped away from his unit before but always returned.
While U.S. officials have hailed his safe return after a long and grueling captivity - he was reported to have been kept in a cage by his militant captors - General Martin Dempsey, chairman of the U.S. Joint Chiefs of Staff, has said the Army would not "look away from misconduct if it occurred."
The investigating general's appointment was first reported by CNN. It is unclear how long the investigation will take.
Bergdahl, who late last week was described as being in stable condition, is being treated by specialists at a military hospital that has been helping returned prisoners of war for decades.