Drummer Lee Rigby of the 2nd Battalion the Royal Regiment of Fusiliers is the soldier killed in the London machete attack near Woolwich Barracks.
Lee Rigby, 25, from Manchester, leaves behind a two-year-old son.
Two men are under arrest in hospital after police shot them near Woolwich Barracks on Wednesday afternoon, in the aftermath of the attack.
The suspects, believed to include Michael Adebolajo, were known to security services, sources have said.
The victim’s name was announced by the Ministry of Defence (MoD) pending formal police identification.
“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 MoD statement said.
“He was a passionate and life-long Manchester United fan.”
Lee Rigby had joined the Army in 2006, and is described as a “loving father to his son Jack” and someone who would be “sorely missed by all who knew him”.
He had taken up a post with the Regimental Recruiting Team in London in 2011.
“An experienced and talented side drummer and machine gunner, he was a true warrior and served with distinction in Afghanistan, Germany and Cyprus,” said 2nd Fusiliers commanding officer Lt Col Jim Taylor.
“His ability, talent and personality made him a natural choice to work in the recruiting group.”
Capt. Alan Williamson said: “Drummer Rigby or <<Rigger>>’ as he was known within the platoon was a cheeky and humorous man, always there with a joke to brighten the mood.”
Defence Secretary Philip Hammond said: “This was a senseless murder of a soldier who has served the Army faithfully in a variety of roles including operational tours in Afghanistan.
“Our thoughts today are with his family and loved ones who are trying to come to terms with this terrible loss.”
Speaking earlier outside 10 Downing Street, PM David Cameron said the attacks were “solely and purely” the responsibility of the individuals involved.
Philip Hammond was asked if the attack showed how vulnerable soldiers were, whether they were in uniform or not.
He replied: “I think it reminds us how vulnerable we all are, but it also reminds us, by the response of the public, that we are not going to be cowed by this kind of terrorist action.”
Chief of Defence Staff General Sir David Richards said: “It’s always a tragedy, it’s particularly poignant that it happened on the streets of this capital city of ours.
“We’re absolutely determined not to be intimated into not doing the right thing – whether it’s here in this country or in Afghanistan or wherever we seek to serve the nation.”
Security at Woolwich Barracks and others in London has been increased, and Gen. David Richards said: “I’m confident that base security is as tight as it’s every been, and necessarily so.
“It’s a very difficult balancing act. We are very proud of the uniform we wear, we have huge support around the country, this is a completely isolated incident.”
Shortly after the killing a man, thought to be 28-year-old Michael Adebolajo, was filmed by a passer-by, saying he carried out the attack because British soldiers killed Muslims every day.
Sources said reports the men had featured in “several investigations” in recent years – but were not deemed to be planning an attack – “were not inaccurate”.
It appears that Michael Adebolajo, a Briton of Nigerian descent, comes from a devout Christian family but took up Islam after leaving college in 2001.
Since British forces intervened in Iraq and Afghanistan, they and their families have been well aware they might be targets at home.
At least two plots by Islamist extremists to kill soldiers in the UK have been foiled in recent years.