Senior US officials told the BBC the name of the suspect as he was heading back to the US to face charges.
He has now arrived at a military detention centre in Fort Leavenworth, Kansas, after being flown from Kuwait, the US Army said.
He will be held in solitary confinement pending charges, the Army added.
Sgt Bales’ lawyer, John Henry Browne, said he had been injured twice while serving in Iraq.
Mr Browne also said the accused, aged 38, had witnessed his friend’s leg blown off the day before the killings.
The US has stressed it remained committed to Afghan reconciliation.
Shortly after Sgt Bales’ name emerged, Mr Browne confirmed that was the name of the soldier he was representing.
Sgt Bales has not yet been charged, but is the only known suspect in the killings – despite repeated Afghan assertions that more than one American was involved.
The Pentagon has previously said that he could face charges that carry a possible death penalty.
Such a trial could take years, contrasting with Afghan demands for swift and decisive justice.