Army Times reported the six soldiers will receive non-judicial punishment, avoiding courts-martial.
Separately three Marines accused of urinating on the bodies of dead Taliban also will avoid courts-martial and receive non-judicial punishment.
The decision means the names of the troops involved will not be released and the specific punishments -- which typically include reduction in rank, confinement to base, extra duty and/or fines -- will not be released, Army Times said.
There was no immediate response from Afghan President Hamid Karzai.
A military investigation of the Koran burnings found six U.S. soldiers at Bagram Airfield were derelict but meant no ill-will when they boxed copies of the Koran and other religious books to go to a landfill to be burned. The investigation also determined the service personnel didn't follow proper procedure when they ordered prison library books destroyed, military officials said.
Both incidents led to violence in Afghanistan, including several deaths.
U.S. military officials said Karzai was briefed about the investigations and their findings. To try to blunt any possible backlash in Afghanistan, coalition officials spent several days talking to political and religious leaders in advance of the announcement.