In a three-minute televised speech, Bush said he had a message for the Iraqi people:
"You will not have to fear the rule of Saddam Hussein ever again."
"In the history of Iraq, a dark and painful era is over. A hopeful day has arrived. All Iraqis can now come together and reject violence and build a new Iraq," Bush said.
"The capture of this man was crucial to the rise of a free Iraq. It marks the end of the road for him, and for all who bullied and killed in his name," he added.
But Bush cautioned that the detention of the former Iraqi president Saddam Hussein did not mean that attacks against US soldiers would come to an end.
Earlier on Sunday a US occupation soldier was killed while trying to detonate a bomb, US central command confirmed.
Saddam was captured on Saturday night near his hometown of Tikrit, hiding in a so-called "spider hole".
US occupying administrator, Paul Bremer, said Saddam was captured late on Saturday 13 December, after more than eights months of searching for him.
Bremer began the press conference with the dramatic announcement, "Ladies and gentlemen, we got him."
Audience members interrupted
Bremer with cheers
His statement was greeted by jubliant applause and cries from some Arab journalists in the audience.
US forces commander in Iraq, Lieutenant General Ricardo Sanchez, also told the news conference that Saddam put up no resistance when he was found hiding in a three metre deep hole on an isolated farm, and was cooperating with his captors.
Sanchez said that the army had received intelligence late on Saturday of two possible hideouts near the village of Adwar.
About 600 special forces participated in the raid to capture the ousted Iraqi leader, who was found hiding in what Sanchez called "a spider hole". He had $750,000 with him and was not injured.
The hole, camouflaged in brick and dirt, had an "air vent and exhaust fan built in... to allow him to remain underground," said Sanchez.
Saddam is now "under coalition custody at an undisclosed
location," Sanchez said, adding the former Iraqi president appeared a "tired man and also I think a man resigned" when captured.
US forces showed a videotape of the hideout. The video showed a bearded Saddam, recieving a medical examination, to the applause of the journalists. Some members of the audience shouted "Death to Saddam" when they saw the video.
In the Iraqi capital, celebratory gunfire rang out, radios played festive music, drivers honked their horns and passengers on buses and trucks chanted "They got Saddam, they got Saddam!"
US troops stationed around Iraq cheered when they heard the news.