During the address Mr. Bush assured Iraqis that "the government of Iraq and the future of your country will soon belong to you."
The messages from Mr. Bush and Mr. Blair were beamed into Iraq via a new Arabic TV network, produced by the U.S. and UK governments, called Nahwa Al-Hurrieh or "Towards Freedom."
The leaders' messages launched the network, which will be broadcast from a U.S. Air Force plane flying over the country. Programming will come from the U.S. and British military as well as rebroadcasts from independent news outlets in both countries, White House officials said.
Starting Saturday, the coalition also will publish a newspaper in southern Iraq, with an initial circulation of 10,000, according to the White House.
The leaders' statements were a bid to reassure ordinary Iraqis of Anglo-American intentions and hasten the full collapse of Saddam's power structure.
"Saddam Hussein's regime is collapsing and the years of brutality, oppression and fear are coming to an end," Mr. Blair said. "We did not want this war but in refusing to give up his weapons of mass destruction, Saddam gave us no choice but to act. Now that the war has begun, it will be seen through to the end."
"You deserve better than tyranny and corruption and torture chambers ... Your nation will soon be free," President Bush said.
"The nightmare that Saddam Hussein has brought to your nation will soon be over," he added.
The two men recorded their messages two days ago at a summit in Northern Ireland.
Aware of suspicions throughout the Arab world of American and British "imperialist" intentions, the two leaders promised troops would leave Iraq as soon as a new government was set up to replace an interim authority due to take over from the military.
President Bush assured Iraqis that the goals of the coalition forces "are clear and limited."
"Coalition forces will help maintain law and order so that Iraqis can live in security. We will respect your great religious traditions, whose principles of equality and compassion are essential to Iraqi's future. We will help you build a peaceful and representative government that protects the rights of all citizens. And then our military forces will leave," Mr. Bush told the Iraqis.
"Iraq will not be run by Britain or by the United States, or by the United Nations. It will be run by you," Mr. Blair said.
The British leader acknowledged many Iraqis feared a repeat of the aftermath of the 1991 Gulf War when Washington urged Saddam's opponents to rise up but did not back them with troops.
"You thought Saddam's rule was being ended, but he stayed, and you suffered. That will not happen this time. This regime will be gone and ended," Mr. Blair said.