Brigadier Saunders aged 53, who had two daughters aged 15 and 14, had served in Northern Ireland between December 1981 and January 1984.
Military attache Brigadier Stephen Saunders was fatally injured when he was shot in his car in Athens.
Brigadier Saunders aged 53, who had two daughters aged 15 and 14, had served in Northern Ireland between December 1981 and January 1984.
After that he was a deputy commander at the Northern Ireland headquarters of the 8th Infantry Brigade.
Greek police are now virtually certain the killing, by two gunmen on a motorcycle, was carried out by left-wing guerilla group November 17.
Ballistic tests revealed that the gun used had been used by the group in past attacks.
November 17 has killed 23 people, including Brigadier Saunders, since it first appeared in 1975. None of its members have been caught.
British Prime Minister Tony Blair described the killing as an act of terrorism which was contemptible as well as senseless.
"His murder is a reminder of the risks that British military personnel face in many places around the world," he added.
British Foreign Secretary Robin Cook said he was "shocked" by the shooting.
"I am in touch with the Greek authorities and am offering them our full co-operation in making sure that whoever perpetrated this brutal attack is brought to justice," he said.
The two gunmen opened fire on Brigadier Saunders around 0800 (0500 GMT) as the British official drove a white Rover belonging to the embassy along Kifissias avenue in a northern suburb.
It appears that the car the Brigadier was driving was not bullet proofed.
Brigadier Saunders suffered four gunshot wounds to the abdomen, the hospital said.
Guerrillas suspected
The gunmen fled and there has been no immediate claim of responsibility for the attack.
Police said they found four spent cartridges at the scene from a .45-calibre pistol, the weapon used by the November 17 group in about 20 assassinations attributed to the group since 1975.
Shadowy group
The November 17 group targets western officials and economic targets. Its first victim, in 1975, was the CIA station chief in Athens.
None of its members has ever been arrested and convicted.
The US State Department has recently criticised the Greek authorities for failing to stop terrorist attacks.
Greek Foreign Minister George Papandreou has condemned the attack and pledged that his government would combat terrorism relentlessly.
"I want to condemn this terrorist act. The act is not only condemned by the Greek government but by all the Greek people," he said.