The two men shot and detained at the scene of Wednesday's attack remained under guard at separate hospitals in London.
The new suspects, identified only as a man and woman, both 29, were being questioned at a police station, Scotland Yard said in a statement Thursday.
Britain's defence ministry said the slain soldier was Drummer Lee Rigby, 25, a Manchester native attached to the 2nd Battalion of the Royal Regiment of Fusiliers.
He is survived by a two-year-old son, Jack.
The two suspects grabbed at the crime scene allegedly used a car to knock down the soldier, who was walking outside a military barracks in London's Woolwich neighbourhood, and then hacked him to death in broad daylight as witnesses looked on.
In video footage aired by Britain's ITV News, one of the suspects - speaking directly into the camera and holding a machete-type knife in his bloodstained hands - alluded to the deployment of Western forces in places like Iraq and Afghanistan in justifying the attack.
"By Allah, we swear by the Almighty Allah that we will never stop fighting you until you leave us alone." the man said. "We must fight them as they fight us, an eye for an eye and a tooth for a tooth."
The two assailants are British citizens of Nigerian origin.
Media outlets identified one of them as Michael Adebolajo, 28, who was raised as a Christian but later converted to Islam and is said to have become radicalized about a decade ago.
British Prime Minister David Cameron said Thursday that "nothing in Islam" justified the brutal killing of Rigby.
In a statement outside his official residence at 10 Downing Street, he said Britain would be "absolutely resolute in its stand against violent terrorism and extremism".
"The people who did this were trying to divide us," the conservative prime minister said. "They should know something like this will only bring us together and make us stronger."
The Muslim Council of Britain roundly condemned the attack in a statement, calling the killing "a barbaric act that has no basis in Islam".
Wednesday night, two people were arrested for attempted attacks on mosques in England, while the far-right English Defense League street movement clashed with police during an anti-Islam demonstration in Woolwich.