The footage appears to contradict Mr Bush's later claims that the scale of the damage took officials by surprise.
Obtained by the Associated Press and broadcast on TV networks today, it shows federal staff and experts telling the president that Katrina could breach levees in New Orleans, putting lives at risk.
Mr Bush listened but did not ask questions during the briefing on August 28 - a day before Katrina hit the Gulf coast. He told state officials: "We are fully prepared."
Four days after the storm devastated New Orleans, however, the president declared: "I don't think anybody anticipated the breach of the levees." The breach sent deadly floodwaters pouring into the city.
He later sought to clarify that statement, saying officials had incorrectly believed the levees had survived Katrina.
Linked by secure video, Max Mayfield, of the National Hurricane Centre, voiced "very, very grave concern" about the levees during the August 28 briefing.
The then Federal Emergency Management Agency chief, Michael Brown, told Mr Bush and the Homeland Security Secretary, Michael Chertoff, that he feared there were not enough disaster teams to help evacuees at the city's Superdome.
Mr Brown faced fierce criticism over his reaction to the storm, and resigned as the director of Fema two weeks after Katrina hit New Orleans.
"We're going to need everything that we can possibly muster, not only in this state and in the region, but the nation, to respond to this event," he said. He urged federal agencies to cut through red tape to help people, bending rules if necessary.
Mr Bush received the briefing at his ranch in Texas. The White House deputy chief of staff, Joe Hagin, sat next to him, but neither asked questions.
"I want to assure the folks at the state level that we are fully prepared to not only help you during the storm, but we will move in whatever resources and assets we have at our disposal after the storm," the president said.
Despite the warnings, the government did not send active duty troops to augment the National Guard in Louisiana until days after Katrina.
Although the taped briefing shows Mr Brown expressing concern that hospitals were not being evacuated, it took days for search and rescue teams to reach some of them after Katrina struck.
Mr Brown told colleagues he was worried about whether evacuees sent to the Superdome would be safe and have adequate medical care - but it took four days for a large-scale evacuation of the stadium to begin to begin.
In the meantime, images of thousands of people stranded there without enough food, water or medical supplies shocked the world.
The New Orleans mayor, Ray Nagin - a fierce critic of the Bush administration's response to the disaster - watched the taped briefing on an AP reporter's camera yesterday.
"I have kind of a sinking feeling in my gut," he said. "I was listening to what people were saying - they didn't know, so therefore it was an issue of a learning curve.
"You know, from this tape it looks like everybody was fully aware."
The White House urged Americans not to read too much into the footage. "I hope people don't draw conclusions from the president getting a single briefing," the presidential spokesman, Trent Duffy, was quoted as saying by AP.
"He received multiple briefings from multiple officials, and he was completely engaged at all times."
