The attack took place near the Royal Artillery Barracks in Woolwich Wednesday afternoon, police said.
The two attackers were carrying weapons and were shot by police arriving on the scene. They were taken to separate hospitals for treatment, Metropolitan Police Commander Simon Letchford was quoted as saying by Xinhua.
"At approx 1420, we were called to reports of an assault in John Wilson Street, Woolwich where one man was being assaulted by two other men. A number of weapons were reportedly being used in the attack, and this included reports of a firearm," Letchford said.
The attacked man was later pronounced dead, with media reports saying he was a soldier.
The ministry of defence has not confirmed the information.
According to local media reports, British government sources said the attack could be "terror related".
Prime Minister David Cameron said the killing in Woolwich was "truly shocking", and asked Home Secretary Theresa May to chair an emergency security meeting.
Cameron will cut short a visit to France to deal with the incident.
"I have been briefed by the Home Secretary on Woolwich shooting and I will return to London tonight (Wednesday) after meeting Hollande," Cameron said.
The prime minister met with French President Francois Hollande.
Cameron said there were strong indications that the attack was a terrorist incident.
"It is the most appalling crime. The police are urgently seeking all facts about this case. There are strong indications that it is a terrorist incident," Cameron said at a press conference with Hollande.