The two choices are likely to stoke controversy as he fills out his second-term national security team.
The selection of Hagel, a maverick former senator and decorated Vietnam veteran tapped to replace Leon Panetta at the Pentagon, appears destined for a bruising Senate confirmation battle against critics who have already launched an onslaught over his record on Israel and Iran.
Obama could also face opposition from human rights groups over his choice of Brennan, a CIA veteran who withdrew from consideration for the spy agency's top job in 2008 after questions were raised about his views on enhanced interrogation techniques used on terrorism suspects during the Bush administration.
Brennan’s parents emigrated to the States from Roscommon.
He would succeed retired General David Petraeus, who resigned amid a scandal over an extramarital affair with his biographer.
Obama, newly returned from his Hawaii vacation, will announce the two nominations at the White House on Monday afternoon, a senior administration official said. A "personnel announcement" was scheduled for 1:05 p.m. EST (1805 GMT).
The addition of Hagel and Brennan, along with Senator John Kerry as nominee for secretary of state, would round out Obama's national security team as he faces daunting challenges of winding down the war in Afghanistan, dealing with the Iranian nuclear standoff and curbing military spending.
Obama is backing Hagel for the Pentagon post despite the fact that the former Nebraska lawmaker, even before being nominated, had become a lightning rod for criticism from the left and the right.
Former Republican colleagues have joined pro-Israel groups and neoconservatives in questioning his commitment to Israel's security and slamming disparaging remarks about what he once called a "Jewish lobby" in Washington.
He has also come under fire for saying in 1998 that a nominee for an ambassadorial post was not qualified because he was "openly, aggressively gay" - a remark for which he has since apologized.
Obama's nomination of Hagel suggests that the president did not want to appear weak by seeming to bow to political opposition and being forced to pick someone other than his favorite contender for a top Cabinet post.
He backed down last month from a tough Senate confirmation battle over Susan Rice, the U.S. ambassador to the United Nations, his first pick to replace Hillary Clinton as secretary of state, and instead settled on Kerry.
But the risk for Obama is that pushing Hagel's nomination could force him to expend political capital he needs more for his next round of fiscal showdowns with congressional Republicans.
The White House is confident it can weather criticism of Hagel's record, get his nomination through the Senate committee that will consider it and win confirmation in the Democratic-led chamber, a source to the nomination process said.
Hagel - who bonded with Obama during their senatorial days over their joint opposition to the Iraq war - would give a bipartisan cast at the highest level of Obama's Cabinet.
But in recent weeks a number of prominent Republicans have said they would oppose Hagel, who has often been at odds with his own party on foreign policy and fiscal matters.
Republican lawmakers made clear on Sunday he would face a difficult nomination process.
"This is an in-your-face nomination by the president to all of us who are supportive of Israel," South Carolina Republican Senator Lindsey Graham told CNN's " State of the Union." "I think it's an incredibly controversial choice."
Critics contend that Hagel, who left the Senate in 2008, at times opposed Israel's interests, voting several times against U.S. sanctions on Iran. But Hagel's supporters insist he has a strong pro-Israel record.
An editorial in The Washington Post last month said that given the scale of the cuts Hagel seeks, he was "not the right choice" for defense secretary.
Senate Republican leader Mitch McConnell said "there would be a lot of tough questions of Senator Hagel."
"If President Obama trusts him, I think Senator Hagel has the experience. He's certainly got the qualities as a person," said McChrystal, a former top U.S. commander in Afghanistan who resigned in 2010.
The nomination of Brennan, who has served as Obama's chief White House counterterrorism adviser since the start of his first term, could also make waves in Washington.
Brennan was believed to have been Obama's top pick to lead the CIA when he took office. But human rights advocates contended that as a senior CIA official under President George W. Bush, Brennan was tainted by the agency's use of interrogation techniques like waterboarding that are widely considered to be torture.
Brennan denied any connection to the interrogation methods but removed his name from consideration.
Brennan, who has a close relationship with Obama, has since won praise for his role in helping to plan the 2011 raid in Pakistan that killed Osama bin Laden, something his supporters hope will quell criticism and keep his nomination on course.
" John Brennan's career of service and extraordinary record has prepared him to be an outstanding director of the CIA. ... Brennan has the full trust and confidence of the president," the senior administration official said. "For four years, he has seen the president every day, and been by his side for some of his toughest decisions."