The video was made public by Wikileaks, which promotes the leaking of information to fight government and corporate corruption, in April when it posted it on the website collateralmurder.org.
The first charge against Manning is for violating army regulations by "transferring classified data onto his personal computer and adding unauthorised software to a classified computer system," the statement said.
The second charge says the soldier, who has been in custody since May 29, is also accused of "communicating, transmitting and delivering national defence information to an unauthorised source".
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While the charging document doesn't mention Wikileaks, Manning is accused of giving the video and at least one cable "to a person not entitled to receive" them.
The charges were brought under the military code of justice and could result in a trial by court-martial.
The gunsight video shows an attack by a US Apache helicopter on a group of men in a square in Baghdad.
It includes audio of the conversations between the Apache helicopter pilots and controllers in which they identified the men in Baghdad as armed fighters and asked for permission to open fire.
"Look at those dead bastards," one person is heard saying in the recording, to which another replied: "Nice".
Shortly after the initial shooting, a van arrived to pick up the dead and wounded and it was fired upon by the Apaches. Two children in the van were injured and later evacuated by US ground troops.
Among those killed in the incident were Namir Noor-Eldeen, 22, a Reuters photographer, and his assistant and driver, Saeed Chmagh, 40.
The families of the two Reuters journalists, who said they have until now received no compensation for the incident, have demanded that the Americans responsible should stand trial.
After the graphic footage was released, the White House described the incident as "tragic" and insisted that US forces in war zones took pains to avoid civilian casualties.
Technology magazine Wired initially reported Manning's arrest and described him as an intelligence analyst who came under suspicion after he told a former hacker during an email exchange that he had leaked the video.
Wired said Manning had also claimed to have leaked other classified information, including video of a 2009 bombing in Afghanistan that killed dozens of civilians, and 260,000 classified US diplomatic cables.
At the time Wikileaks said only that it had obtained the video "from a number of military whistleblowers" and had been able to view and investigate it after breaking an encryption code, but did not provide any further information on how it got hold of it.
On Tuesday, it announced the news of Manning's indictment, saying; "Private Manning charged with disclosing Iraq-slaughter video. Trigger happy Apache crew remain uncharged."