The hostages were found tied up in the same room of a house in western Baghdad, said coalition forces spokesman Major General Rick Lynch.
The kidnappers were not caught during the raid and operations are continuing, he added.
Maj Gen Lynch told reporters in Baghdad: "Late last night, coalition forces conducted an operation and it came up with two detainees.
"These two detainees provided actionable intelligence about the location of the Christian Peacemaker Team hostages.
"We got that information at eight o'clock this morning and we conducted the operation.
"We moved to the location in western Baghdad that was reported for the location of the Christian Peacemaker Team.
"We conducted an assault on the house and inside the house we found the three hostages, in good condition.
"There were no kidnappers there at the time. The three hostages were by themselves."
The hostages were then freed, debriefed and taken to a hospital for medical checks.
"The key point is it was intelligence-led. It was information provided by a detainee," he said.
"In this particular case, of those two detainees, one knew where the hostages were and provided that information.
"The operation was planned and executed and the effect was the safe return of the three hostages."
Maj Gen Lynch said the hostages were "bound" but were found to be in "relatively good condition".
"They were bound. They were together. There were no kidnappers in the area," he said.
"There seems to be a kidnapping cell that has been robust over the last several months in conducting these kind of kidnappings.
"It was a coalition forces operation so it involved all sorts of members of the coalition.
"The size and magnitude of the operation I'm not going to walk you through, because we have got other operations that continue."
Skilled personnel from Britain, Canada, the US and Iraq launched a daring raid on a secret hideout to free Briton Mr Kember, 74, along with Canadians James Loney, 41, and Harmeet Singh Sooden, 32.
Weeks of planning and collecting vital information helped end their 118-day kidnap ordeal without a shot being fired.
Former SAS soldier Andy McNab said: "The most important weapon in these types of operations is not what we call the 'bang-bang' at the end of the operation, it is the information that is built up.
"It is really detailed information. It is not just the hostage and what building he is in but where exactly in the building he is.
"It is all about speed, aggression and surprise. You have got to get in there and get them out before there is any reaction from the hostage takers."
The early morning operation took place in a rural area north west of Baghdad, between the towns of Mishahda, 20 miles north of Baghdad, and the western suburb of Abu Ghraib, 12 miles from the city centre.
Foreign Secretary Jack Straw would not comment on which British military unit was involved, leaving many to believe the SAS were part of the rescue mission.
Mr Straw said: "British forces were involved. It follows weeks and weeks of very careful work by our military and coalition personnel in Iraq and many civilians as well."
The final hours and minutes before such operations are crucial to their success and fraught with danger.
Soldiers have been known to wait in the darkness outside the target building for 20 minutes, trying to keep hidden so as not to compromise the raid.
Speaking to BBC News 24, Mr McNab said that during the actual snatch the hostages can expect to be treated quite aggressively by their rescuers.
This is the best way to keep control of people who are possibly frightened, weak or excited that they have a chance of freedom.
Mr McNab said: "A lot of hostages see their rescuers and tend to grab them as a form of security, so they are secured quite aggressively.
"You have to get them out of the danger area, get them in a holding pen, confirm that you have got the right guys and then they can move on to get medical attention and consequently be released."
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