Obama, during the nearly 30-minute announcement, called the men patriots who understand that "we are only successful because of the folks up and down the line" in the Defense Department and the Central Intelligence Agency.
Hagel, a Republican who once represented Nebraska in the U.S. Senate, "is the leader our troops deserve," Obama said. "He is an American patriot."
If his nomination is approved by the Senate, Hagel would be the first enlisted man, and first Vietnam-era veteran, to lead the Defense Department. He would succeed Leon Panetta.
Men and women in uniform would see Hagel as a "combat vet of character and strength ... one of their own," Obama said.
"Chuck knows war is not an abstraction," the president said. "He understands sending young Americans to fight ... and bleed ... is something we do only when necessary."
Hagel said he was grateful for the opportunity to strengthen the country's military posture, its alliances and "to help build a better world for all mankind. I will do my best."
Hagel, who was awarded the Purple Heart twice, likely will face tough questioning during the confirmation process as senators from both sides of the aisle expressed reservations.
Hagel "would be the most antagonistic secretary of defense toward the state of Israel in our nation's history," Sen. Lindsey Graham, R-S.C., said Sunday on CNN's "State of the Union."
"He has long severed his ties with the Republican Party," Graham said. "This is an in-your-face nomination by the president to all of us who are supportive of Israel. I don't know what his management experience is regarding the Pentagon -- little, if any -- so I think it's an incredibly controversial choice."
Some Democrats have said they are wary of comments Hagel made in 1998 when he questioned whether "openly, aggressively gay" James Hormel was appropriate to be President Bill Clinton's ambassador to Luxembourg.
Brennan, Obama said, is a tireless public servant whose "integrity and commitment to values defines us as Americans. If confirmed, Brennan would succeed Acting CIA Director Michael Morell, who assumed the directorship when David Petraeus resigned after an extramarital affair came to light.
If Brennan earns Senate approval, which he is expected to do easily, the men and women of the CIA will have one of their own, Obama said.
"He knows you ... cares for you ... and will fight for you every single day."
Brennan said CIA agents "need and deserve the support of all their fellow Americans." He said if he is confirmed he will "make it my mission" to keep the country safe.
Obama called on the Senate to confirm the two men without delay because "when it comes to national security, we don't like to leave a lot of gaps."