Mr Green, who is being held in the US, denies the rape and murder charges.
A fifth soldier serving in Iraq has been charged with dereliction of duty for failing to report the offences.
The US military did not release the names of the soldiers charged in Iraq. They are all infantrymen from the 101st Airborne division, one of the elite US army units.
A statement said they would face an Article 32 investigation, similar to a grand jury hearing in civilian law.