Army officials said Lee Rigby, 25, nicknamed Riggers, was married with a 2-year-old son, The Guardian reported. He enlisted in 2006 and was deployed to Afghanistan in 2009.
Rigby, apparently targeted because he was wearing a T-shirt for the soldiers' charity Help for Heroes, was hacked to death Wednesday outside the Royal Artillery Barracks in the Woolwich district of London.
The alleged knife-wielding assailants then waited about 20 minutes, milling about the scene, shouting at bystanders whom they asked to record the incident, until armed police arrived.
Police shot and wounded the suspects, officials said. The men were in separate hospitals under police guard Thursday, one listed in serious condition.
One of the men shouted "Allahu akbar" -- "God is great" -- during the attack, government officials said.
The Ministry of Defense released a statement detailing Rigby's career, which included tours in Cyprus and Germany and service with the guard outside royal palaces in London.
"An extremely popular and witty soldier, Drummer Rigby was a larger than life personality within the Corps of Drums and was well known, liked and respected across the Second Fusiliers," the Ministry of Defense said in a statement. "He was a passionate and life-long Manchester United fan."
Police searched houses in London and elsewhere occupied by relatives of Michael Adebolajo, believed to be one of the suspects in the killing, police said. A woman who said she had gone to school with Adebolajo told the Guardian he was a "down-to-earth nice guy."
The woman, who gave her name only as Louise, said Adebolajo's mother was strict and a regular church-goer. But she said Adebolajo in his late teens became involved with Nigerian criminal gangs in London.
About 250 supporters of the English Defense League street protest movement, all wearing black ski masks and some in paramilitary dress, descended on Woolwich late Wednesday and threw rocks and bottles at police. The rioting occurred blocks from the site of the killing.
"They're chopping our soldiers' heads off. This is Islam. That's what we've seen today," English Defense League leader Tommy Robinson was quoted by the London Evening Standard as saying late Wednesday during the melee.
British Prime Minister David Cameron cut short a trip to France after learning of the attack.
"We obviously are urgently seeking and the police are urgently seeking the full facts about this case, but there are strong indications that it is a terrorist incident," Cameron said at the Elysee Palace in Paris, where he was meeting EU leaders.
He called the killing "an appalling murder" and "absolutely sickening" and said, "We've had these sorts of attacks before in our country, and we will never buckle in the face of them."
If confirmed as an act of terrorism, it would be the first fatal attack in Britain since 52 people were killed in four coordinated suicide bombings targeting London's transit system July 7, 2005.
British Home Secretary Theresa May held an emergency Cabinet meeting about the attack Wednesday evening.