These are the first suicides at the base, despite dozens of attempts
The camp commander said the two Saudis and a Yemeni were "committed" and had killed themselves in "an act of asymmetric warfare waged against us".
Lawyers said the men who hanged themselves had been driven by despair.
A military investigation into the deaths is now under way, amid growing calls for the detention centre to be moved or closed.
Walter White, an international lawyer who specialises in human rights, told the BBC the Guantanamo camp was likely to be considered a "great stain" on the human rights record of the US.
There have been dozens of suicide attempts since the camp was set up four years ago - but none successful until now.
The men were found unresponsive and not breathing by guards on Saturday morning, said officials.
They were in separate cells in Camp One, the highest security section of the prison.
I believe this was not an act of desperation, but an act of warfare waged against us
Rear Adm Harry Harris
Camp commander
They hanged themselves with clothing and bed sheets, camp commander Rear Adm Harry Harris said.
He said medical teams had tried to revive the men, but all three were pronounced dead.
'Creative'
Rear Adm Harris said he did not believe the men had killed themselves out of despair.
"They are smart. They are creative, they are committed," he said.
"They have no regard for life, either ours or their own. I believe this was not an act of desperation, but an act of asymmetrical warfare waged against us."
If it's perfectly legal and there's nothing going wrong there - well, why don't they have it in America?
Harriet Harman
UK Constitutional Affairs Minister
All three men had previously taken part in some of the mass on-and-off hunger strikes undertaken by detainees since last August, and all three had been force-fed by camp authorities.
They had left suicide notes, but no details have been made available.
The US military said the men's bodies were being treated "with the utmost respect".
White House spokesman Tony Snow said Mr Bush had "expressed serious concern" at the deaths.
"He also stressed that it was important to treat the bodies humanely and with cultural sensitivity," he said.
A spokesman for UK Prime Minister Tony Blair described the suicide as a "sad incident".
'Heroes'
UK Constitutional Affairs Minister Harriet Harman told the BBC on Sunday the camp should be moved to the US or shut down.
"If it's perfectly legal and there's nothing going wrong there - well, why don't they have it in America and then the American court system can supervise it?" she said.
HAVE YOUR SAY We are losing credibility with our friends and allies
Jim, Pinehurst, USA
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William Goodman from the New York-based Center for Constitutional Rights told AFP news agency the three dead men were "heroes for those of us who believe in basic American values of justice, fairness and democracy".
Mr Goodman, whose organisation represents some 300 detainees, said the government had denied them that.
Ken Roth, head of Human Rights Watch in New York, told the BBC the men had probably been driven by despair.
"These people are despairing because they are being held lawlessly," he said.
"There's no end in sight. They're not being brought before any independent judges. They're not being charged and convicted for any crime."
On Friday, Mr Bush said he would "like to end Guantanamo", adding he believed the inmates "ought to be tried in courts here in the United States".
File image of detainees upon arrival at , January 2002
Lawyers asked a federal court Friday to allow the government to inspect written materials that it seized from inmates at Guantanamo Bay last month and requested approval to use "filter teams" to look at documents that may contain privileged lawyer-client communication.

In documents they filed with the , government lawyers argued that three inmates who committed suicide last month by hanging themselves coordinated their actions by using attorney-client confidentiality to communicate with each other. Government officials said that among papers marked "Attorney Client Privilege" were instructions on how to tie knots and a classified memo on camp activities and inmate locations.

Military officials seized more than 1,100 pounds of documents from inmates after the suicides on June 10.  They have since stopped defense lawyers from sending any documents to inmates.

In an affidavit that lawyers for the government filed with the court, Rear Admiral Harry B. Harris Jr., the naval commander of the camp, described evidence of a "larger plan or pact for more suicides" among detainees.  His statement implied that the investigation might extend to defense attorneys as third parties who "encouraged, ordered or assisted" the detainees in killing themselves.  

Harris earlier described the suicides as part of a pattern of hostile actions on the part of terror suspects. "They have no regard for life, either ours or their own," he said last month. "I believe this was not an act of desperation, but an act of asymmetrical warfare waged against us." 

The , which has provided legal assistance to about 200 Guantanamo detainees, has been critical of the conditions at Guantanamo Bay that they say finally led the detainees to kill themselves in desperation.

Barbara Olshansky, a deputy legal director at CCR, described the government's latest legal activity as a tactic to impede detainees' access to legal representation "and to make these lawyers fight for yet another thing."

Last month after the document seizures, defense attorney Richard Wilson, who represents a Canadian detainee, said in an affidavit that the military had told him that they were conducting no investigation into the role of attorneys in the prisoners' deaths.

He added, however, that at least one detainee claimed that camp officials had confiscated his written materials and told him that they were looking into "whether lawyers had actively encouraged detainees to commit suicide."