Yet, Bush said in a statement issued late Friday from his ranch in Texas, "it is an important milestone on Iraq's course to becoming a democracy that can govern, sustain and defend itself, and be an ally in the war on terror."
In a message of assurance to the people of Iraq, Bush said the execution was a reminder of how far the Iraqi people have come since the end of Saddam's rule.
"The progress they have made would not have been possible without the continued service and sacrifice of our men and women in uniform," he said.
Bush, who has spent weeks crafting a new U.S. policy in Iraq, warned of more challenges for U.S. troops.
"Many difficult choices and further sacrifices lie ahead," he said. "Yet the safety and security of the American people require that we not relent in ensuring that Iraq's young democracy continues to progress."
When Saddam was apprehended in 2003, Bush promised that the deposed Iraqi leader would "face the justice he denied to millions." The administration blamed Saddam for hundreds of thousands of mass executions.
In November, Saddam was sentenced to death after being convicted of murder in the killings of 148 Shiite Muslims from an Iraqi town where assassins tried to kill him in 1982.
After three decades in power, Saddam was captured in December 2003 in an underground hideout on a farm near his hometown of Tikrit. Two days later, Bush remarked: "Good riddance. The world is better off without you, Mr. Saddam Hussein."
The president was briefed at 6:15 p.m. CST (00015 GMT) by National Security Adviser Stephen Hadley about the execution procedure, and that it would go forward in the next few hours. Hadley had been in touch with U.S. Ambassador to Iraq Zalmay Khalilzad, who had been in contact with Iraqi Prime Minister Nouri al-Maliki.
CBS News correspondent Mark Knoller reports that Bush was asleep when the execution occurred.
"The president concluded his day knowing that the final phase of bringing Saddam Hussein to justice was under way," deputy White House press secretary Scott Stanzel said.