Barr shares at least one of the president's views on the probe being conducted by special counsel Robert S. Mueller III.
Barr previously served as attorney general under President George H.W. Bush.
The post of attorney general has vexed Mr. Trump since the early days of his presidency, when Mr. Sessions recused himself from overseeing an investigation into possible collusion between Russian Federation and the Trump campaign. Mr. Barr, 68, is a former general counsel and executive vice president of Verizon Communications who works now as a lawyer at the firm of Kirkland & Ellis.
Barr has been on a White House short list of contenders for several weeks, said a person with knowledge of internal discussions who was not authorized to speak publicly.
President Trump said Friday he will nominate William P. Barr as attorney general and Heather Nauert as ambassador to the United Nations. Sessions's chief of staff, Matthew Whitaker, is now serving as acting attorney general.
Mr Barr retired from his position as counsel and executive vice-president of Verizon in 2008.
Barr served in the Bush administration from 1989 to 1993, starting out as an assistant attorney general in charge of the Office of Legal Counsel before becoming the deputy attorney general in 1990.
He also wrote an op-ed for The Washington Post in May 2017 defending Trump's decision to fire former FBI Director James Comey, one of the actions Mueller has been examining for possible obstruction of justice.
The 68-year-old Republican lawyer has an impressive political resume, spanning the CIA, White House and Department of Justice. He has said that Mueller could have been "more balanced" in his choice of prosecutors, a majority of whom have either ties to Democrats or have made donations to them.
Barr, a Columbia University graduate, worked at the Central Intelligence Agency while attending the George Washington University Law School at night.
Barr also raised concerns about special counsel Mueller's appointment of prosecutors with a history of donating to Democratic candidates, telling The Washington Post in July 2017 that he "would have liked to see him have more balance on this group".
Mr Barr holds degrees in government and Chinese studies from Columbia University.