Mr Bush called on the US Senate to confirm the Air Force general promptly.
"Mike knows our intelligence community from the ground up. He has been both a provider and a consumer of intelligence," Bush said at the White House.
"He has demonstrated an ability to adapt our intelligence services to the new challenges of the war on terror," said the US leader, flanked by General Hayden on one side and his director of national intelligence, John Negroponte, on the other.
"He's the right man to lead the CIA at this critical moment in our nation's history."
In accepting the nomination, General Hayden, currently Mr Negroponte's right-hand man, had words of praise for the two CIA directors that immediately preceded him, George Tenet and Porter Goss, who submitted his resignation on Friday.
"I know that I will be standing on their shoulders," General Hayden said.
Appointment criticised
The nomination already has proved controversial, with many in Washington expressing serious doubts about General Hayden's independence from the White House and about whether the career military man will be able to stand up to the increasingly powerful Defence Department.
Top US Republican and Democratic lawmakers have expressed concern over the nomination, setting up a possible congressional battle over the White House.
Some lawmakers were critical of General Hayden's involvement in a controversial domestic spying program.
"Bottom line, I do believe he's the wrong person, the wrong place, at the wrong time," said Republican Representative Pete Hoekstra, who heads the House intelligence committee.
"We should not have a military person leading a civilian agency at this time," he said.
Mr Bush said however that he views General Hayden's military background as an asset, noting that the military officer holds a broad range of vital public experience and intimate knowledge of the landscape of global espionage that will serve him well as CIA chief.
"He's held senior positions at the Pentagon, the US European Command, the National Security Council, and served behind the Iron Curtain in our embassy in Bulgaria during the Cold War," the president said.
"He's overseen the development of both human and technological intelligence. He has demonstrated an ability to adapt our intelligence services to the new challenges in the war on terror."
Hoping to lay to rest persistent rumors that Mr Goss was forced to resign as a result of a rift with the president and Mr Negroponte over policy and continued internal turmoil at the CIA, Mr Bush also heaped praise on the outgoing spy chief as a "great patriot."