"He was my first choice since Day One," Trump told reporters on the White House's South Lawn before he departed for a speech in Kansas City, also calling Barr a "highly-respected lawyer" and "a brilliant man."
"[He is] respected by Republicans and respected by Democrats," he added. "I think he will serve with great distinction."
Barr will require confirmation by the U.S. Senate to get the job and Democrats have already identified contentious points on his resume. He ran the Justice Department when Bush pardoned officials in the Iran-Contra affair controversy.
"If he is the nominee, he will deserve a very rigorous vetting by the Senate," said Norm Eisen, chair of the Citizens for Responsibility and Ethics in Washington. "He has advanced the bizarre idea that Hillary Clinton's role in the Uranium One deal is more worthy of investigation than Trump-Russia collusion. That is nonsense."
Barr would replace Jeff Sessions, who was fired by Trump last month. It also means acting Attorney General Matthew Whitaker will no longer hold the post.
Bush appointed Barr to the top law enforcement post in 1991, where he stayed for 14 months. In 1992, he was criticized for his handling of a banking loan scandal involving Italy's Banca Nazionale de Lavoro.
After serving under Bush, Barr was a corporate executive for 14 years for Verizon.
Before departing, Trump also said he will make another major personnel announcement Saturday.
"I have another one for tomorrow that I'm going to be announcing at the Army-Navy game," he said. "I can give you a little hint: It will have to do with the Joint Chiefs of Staff and succession. And I look forward to telling you."