"The world is hearing the voice of freedom from the centre of the Middle East," the US president told reporters at the White House, four hours after the polls closed.
In a brief statement, during which he took no questions, Mr Bush praised the bravery of those Iraqis who had voted for rejecting the "anti-democratic ideology of the terrorists.
"They have refused to be intimidated by thugs and assassins," he said.
"They have chosen a future of freedom, of peace," he added, before acknowledging that "some Iraqis were killed while exercising their rights as citizens".
Mr Bush went on to praise the contributions of the American and British troops who were killed yesterday, pledging that their lives were not lost in vain.
"Their sacrifices were made in a vital cause of freedom," he said.
The president thanked the American people for being "patient and resolute" but warned that the election would not stop the violence.
"There's more distance to travel on the road to democracy," he said, pledging continued American involvement "so this rising democracy can eventually take responsibility for its own security".
The EU foreign policy representative, Javier Solana, congratulated "the Iraqi people who have shown courage and determination in voting" despite the threat of violence.
"The elections represent an important step forward for Iraq," Mr Solana said in a statement. "Despite the many difficulties that lie ahead, the elections mark progress towards a transition to a democratic, free and peaceful Iraq."
The UN's electoral adviser in Iraq said he was encouraged by the early results of the election.
"If the results are confirmed - and the only reason to be cautious is the lack of a complete picture - then it is very good news. But the challenge is for the results to be accepted by the Sunni minority," Carlos Valenzuela, the UN's electoral adviser in Iraq, told Reuters.
Before the polls had closed in Iraq the US secretary of state, Condoleezza Rice, had declared them a triumph.
Ms Rice said they had gone better than expected, while refusing to elaborate on US predictions for turnout, violence or other factors.
"We all recognise the Iraqis have a long road ahead of them," said Ms Rice. "The insurgency is not going to go away as a result of today, but the Iraqi people have taken a very important step in losing the sense of fear and intimidation that has been in their lives for decades."
The US is spending more than $1bn (£530m) a week in Iraq, and Ms Rice said the US would discuss the continued need for outside security forces with the newly elected Iraqi assembly.
As she toured the talkshow circuit yesterday morning Ms Rice said: "What we're seeing today is what the Iraqis want their future to be. They want it to be one based on democracy - on the vote, not on the gun."
The turnout in the face of violence and threats, she argued, was a reminder that liberty and self-government were "universal values".
The defeated Democratic presidential challenger, John Kerry, added a note of caution in his first televised interview since losing the election in November.
"No one in the United States should try to overhype this election," he said.
"This election is a sort of demarcation point, and what really counts now is the effort to have a legitimate political reconciliation."
What mattered at this stage, said Mr Kerry, was the involvement of more countries to help the US war effort.
The domestic political response to the elections appeared to split down party lines, with Republicans praising the process while Democrats sounded more cautious.