USA media report he has been critical of some aspects of that inquiry.
"I've seen very good things about him even over the last day or so, when people thought it might be Bill Barr [as the nominee]", the president said. Barr is now an attorney for Kirkland and Ellis, a high-profile Washington, D.C., law firm.
If Mr Barr is confirmed by the senate after his official nomination, he will replace the current acting attorney general, Matt Whitaker.
Mr. Barr has been critical publicly of the special counsel's investigation.
Will Democrats derail his appointment?
On paper William Barr looks like a safe pick for U.S. attorney general.
From Verizon Communications to GTE Corporation, Barr spent more than 14 years working in senior corporate positions following his career at the Justice Department, according to his biography.
Barr has criticised Mueller for hiring attorneys for his team who contributed to Democratic politicians, including Hillary Clinton. He's not exactly a drain-the-Washington-swamp choice, but that has never been a priority in the gilded halls of the upper chamber of Congress.
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It's hard to say how all these new changes will affect the game and how players will take to the game-changing new ways to travel. Epic Games has made Fortnite Creative available to Battle Pass owners today (general availability begins next week, on 13 Dec).
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We're not really sure what to expect from Nintendo, but we do know the company is planning an announcement of some sort. Several influencers have received teaser items from Activision including Crash cookies and a pair of fuzzy orange dice.
However, Democrats have hinted that they will make the nomination process a nightmare for Barr, considering his past criticisms about special counsel Robert Mueller's Russian Federation investigation.
More of note than Barr's experience in the role may be comments he made as recently as 2017. Republicans have 53 votes in the Senate and Barr won't be in danger of losing any of them. There will be plenty of fireworks during the confirmation hearing, but the end is not in any doubt at all. This, however, is a nomination that will be hard for Democrats to derail. Mr. Trump broke the news Friday to reporters on the White House South Lawn on his way to Kansas City.
Mr Barr holds degrees in government and Chinese studies from Columbia University.
Barr, a Columbia University graduate, worked at the Central Intelligence Agency while attending the George Washington University Law School at night.
As a young lawyer, he clerked for the DC appeals court.
Barr, 68, served as US Attorney General in 1991-1993. I was happy that GTE's conduct of the litigation was considerably more aggressive than that of other similarly situated carriers who were also required to share their facilities and equipment with new competitors under the Act.
He also said that there would be nothing wrong with then Attorney General Jeff Sessions calling for an investigation into both Clinton and James Comey in regards to Clinton's private email server.