"Judge Mukasey is clear-eyed about the threat our nation faces," Mr. Bush said.
If confirmed by the Senate, Mukasey, a retired federal judge who has handled terrorism cases for more than a decade, would become Mr. Bush's third attorney general. The president said that as chief judge of the busy U.S. District Court for the Southern District of New York, Mukasey presided over high-profile national security cases.
"He knows what it takes to fight this war effectively and he knows how to do it in a manner consistent with our laws and our Constitution," Mr. Bush said, standing next to Mukasey in the Rose Garden.
Mr. Bush urged the Senate to quickly confirm Mukasey.
Mukasey oversaw the convictions of the blind sheik, Omar Abdel Rahman, and 11 others in the 1993 World Trade Center bombing, reports CBS News correspondent Bob Orr. More recently, he supported the president's detention of Jose Padilla as an "enemy combatant" but rejected arguments that the al Qaeda sympathizer be denied a lawyer.
If he gets a nod from the Senate, Mukasey would take charge of a Justice Department where morale is low following months of investigations into the firings of nine U.S. attorneys and Gonzales' sworn testimony on the Bush administration's terrorist surveillance program.
Mukasey said he was honored to be Mr. Bush's nominee to take the helm of the department.
"My finest hope and prayer at this time is that if confirmed I can give them the support and the leadership they deserve," he said.
"I look forward to meeting with members of Congress in the days ahead and, if confirmed, to working with Congress to meeting our nation's challenges," Mukasey said, just before shaking the president's hand and walking back with him into the Oval Office.
It won't be a cakewalk, but Mukasey will likely win Senate confirmation, reports CBS News correspondent Bob Fuss.
New York Democrat Chuck Schumer, who led the charge to oust Gonzales, said that while Mukasey "is certainly conservative," he "seems to be the kind of nominee who would put rule of law first and show independence from the White House - our most important criteria."
Senate Majority Leader Harry Reid said he believes the president listened to Congress and decided against a more partisan replacement for Gonzales. He said Mukasey had "strong professional credentials and a reputation for independence."
"A man who spent 18 years on the federal bench surely understands the importance of checks and balances and knows how to say no to the president when he oversteps the Constitution," said Reid, D-Nev. "But there should be no rush to judgment. The Senate Judiciary Committee must carefully examine Judge Mukasey's views on the complex legal challenges facing the nation."
In picking Mukasey, the president bowed to pressure from Democrats, who had threatened to fight the nomination of any conservative insider, adds Orr.
Last week, top Democrats specifically warned against naming former Solicitor General Ted Olson, who was thought to be at the top of the president's list.
The White House, however, denied that Mr. Bush chose Mukasey to avoid a battle in the Senate.
"It's not the president who is looking for a fight. The Senate Democrats have made the Department of Justice their cause celebre for the past several months and they have decided that that's where they wanted to fight," Perino said. "If they decide to make an issue about this nomination, that will be at their feet and they're going to have to explain that to the American people. ... We're not looking for a fight."
Perino dodged a question about whether the president saw Mukasey as a consensus nominee. "I think what he is is a very solid nominee," she said.
Perino said Mukasey will "bring fresh perspective" to the Justice Department and to the president, reports CBS News correspondent Peter Maer.
Mukasey currently serves as a judicial adviser to GOP presidential hopeful Rudy Giuliani. Perino said that if Mukasey is confirmed, he will sever ties with the Giuliani campaign. Perino said that Mr. Bush offered the nomination to Mukasey on Friday, and he accepted.
Bush critics contended the Mukasey nomination was evidence of Mr. Bush's weakened political clout as he heads into the final 15 months of his presidency. The president's supporters say Mukasey has impeccable credentials, is a strong, law-and-order jurist, especially on national security issues, and will restore confidence in the Justice Department.
Mukasey has drawn lukewarm reviews from some members of the GOP's right flank. Some legal conservatives and Republican activists have expressed reservations about Mukasey's legal record and past endorsements from liberals, and were drafting a strategy to oppose his confirmation.
William Kristol, editor of the conservative Weekly Standard, said some of his fellow conservatives are upset that Olson, the former solicitor general, who represented Mr. Bush before the Supreme Court in the contested 2000 election, was not chosen.
Mukasey, chosen in large part for his experience in national security matters, noted the threat of terrorism in his brief remarks. "Thirty five years ago, our foreign adversaries saw widespread devastation as a deterrent," he said. "Today, our fanatical enemies see it as a divine fulfillment."
Mr. Bush gave a quick, final nod to the departed attorney general, Gonzales, who resigned after months of turmoil and accusations of mismanagement.
"I've known Al and his family for more than a decade," Mr. Bush said. "He's a dear friend and a trusted adviser."
Until a new attorney general is confirmed by the Senate, Mr. Bush said, Assistant Attorney General Peter D. Keisler will serve as acting attorney general. Keisler oversaw the Bush administration's lengthy legal fight over the rights of terrorism war-era prisoners at Guantanamo Bay.
Keisler had announced his resignation from the department in early September. He had been nominated by Mr. Bush earlier in the year for a seat on the U.S. Court of Appeals for the District of Columbia Circuit. The Senate has not acted on Keisler's nomination.
Mr. Bush said that Keisler had agreed to stay on at the Justice Department, which will allow Solicitor General Paul Clement to focus on his duties as the government's chief advocate as the Supreme Court nears the opening of its new fall term.