Eyewitnesses said two men called out "Allahu Akbar [God is Great]" before attacking the victim as he walked along a street in east London, and waved weapons as they dumped his body in the middle of the road, the BBC reported.
The victim was described only as a man in his 20s but Member of Parliament Nick Raynsford said he was a soldier at Woolwich barracks, the report said.
There were conflicting reports on whether the weapon was a machete or a meat cleaver.
Prime Minister David Cameron said there were "strong indications that it is a terrorist incident."
Cameron's office said he would return to London from Paris Wednesday. He had planned to remain in Paris Wednesday night following meetings with French President Francois Hollande.
Home Secretary Theresa May has called emergency response officials to a meeting in the British Cabinet Office Briefing Room and has directed British intelligence and police officials to keep her informed of developments in the investigation, the report said.
The BBC said police think there may be video footage of the attack.
The two alleged attackers shot by police have been hospitalized.
Senior aides to Mayor of London Boris Johnson called the killing a "sickening deluded deranged act of violence," the BBC reported.