The 74-year-old grandfather was in "reasonable condition" and was recovering in the high security Green Zone in Baghdad after his 118-day kidnap ordeal.
Speaking in London, the UK Foreign Secretary Jack Straw said he had spoken to Mrs Pat Kember, who was "absolutely delighted, elated" at the news about her husband.
Mr Straw said the men were freed in a multi-national operation in the town of Mishahda, about 20 miles north of Baghdad.
He said: "British forces were involved in this operation. It follows weeks and weeks of very careful work by our military and coalition personnel in Iraq and many civilians as well."
The UK Defence Secretary John Reid said British troops had "spearheaded" the rescue operation. He told Sky News: "The rescue of Norman Kember and his colleagues this morning was by a multinational force spearheaded by British troops."
He added: "British troops were involved in a rolling operation which finished around 5am this morning. It was several weeks in the planning. The British troops played a key role in it but of course it involved troops from other nations as well."
A Ministry of Defence spokesman declined to comment on reports that soldiers from the SAS were involved.
Very few details emerged of the operation, although a US military spokesman said that none of the hostage-takers had been at the site when the hostages were freed. The three had been bound together and had been in relatively good health. The rescue was based on information from a man captured last night.
Mr Kember, a retired professor and a former medical physicist at a teaching hospital, was seized during a peace mission to Baghdad on 26 November. He is from Pinner, north-west London, and was visiting the country with Christian Peacemaker Teams, a Canada-based international peace group.
The other men taken hostage with him were Canadians James Loney, 41, and Harmeet Singh Sooden, 32, and an American, Tom Fox, 54.
Mr Fox was found shot dead in Baghdad earlier this month in the affluent Mansour district. There were signs that he had been beaten before being killed. The grim news raised the prospect that Mr Kember might meet the same fate.
The news that he had been successfully freed earlier today was greeted with delight.
The Rev Alan Betteridge, a friend of Mr Kember for more than 40 years, said: "We are immensely relieved and thankful, especially after the death of Tom Fox, which made us very fearful.
"We were praying for his release this morning. We have been praying for them every day."
Fellow peace campaigner Bruce Kent, who has been involved in weekly vigils for his release since his capture, said "this is news beyond belief".
He said: "In this awful mess of Baghdad thank God there is one bright light anyway."
Speaking about his friend's ordeal, he added: "It was absolute torture. And thinking of the unfortunate American Tom Fox who was murdered, they must have had the most terrible time."
Ihtisham Hibatullah, of the Muslim Association of Britain, said the group was "greatly relieved" by the news.
Speaking about moves to secure their release, he said: "The hostage takers were ruthless and did not heed this call.
"Now we all feel that this should be the last time in Iraq that anyone should be taken and put through this kind of trauma."
In an interview with Sky News, he said Mr Kember was a "true friend of Iraqis" who had worked for peace.
In a statement, a 10 Downing Street spokesman said: "The Prime Minister is delighted by the news. He is particularly pleased for those released and their families. He congratulates everyone involved in the operation to rescue the hostages."
Mr Kember's brother was overcome with emotion at the news of the release.
Speaking from his home in Taunton, Ian Kember said: "It's fresh news to me, I haven't got my thoughts together yet.
"It's a wonderful thing, and it's obviously a great relief, but beyond that I haven't come to terms with it yet.
"This has been the news we have been waiting for for a long time."
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