President Barack Obama's nominee was confirmed with a 63-34 vote, which came after Paul dropped his objection to moving ahead with Brennan's confirmation vote upon receiving a letter from Attorney General Eric Holder.
The Kentucky senator had mounted the filibuster because he wanted greater clarity on whether the Obama administration has the authority to use lethal force, such as a drone, against a suspected terrorist who is a U.S. citizen.
"Do you have the authority to kill Americans on American soil?" Paul summed up the question for reporters on Thursday.
White House spokesman Jay Carney said the attorney general sent Paul a letter responding to Paul's question. Quoting from the letter, Carney said: "Does the president have the authority to use a weaponized drone to kill an American not engaged in combat on American soil? The answer is no."
The Obama administration has said it has not conducted such operations inside U.S. borders, nor does it intend to.
While Paul got the endorsement of Minority Leader and fellow Kentuckian Mitch McConnell, two senior Republicans on the Armed Services Committee dismissed Paul's claims as unfounded and ridiculous.
"To my Republican colleagues, I don't remember any of you coming down here suggesting that President Bush was going to kill anybody with a drone," Sen. Lindsey Graham of South Carolina said in remarks on the Senate floor.
Graham went on to say that he had originally planned to vote against Brennan's nomination, but he now intends to support the nominee because the confirmation fight has become a referendum on the drone program.
Sen. John McCain scoffed at Paul's contention that the U.S. would have targeted actress Jane Fonda during her trip to Hanoi during the Vietnam War.
"I must say that the use of Jane Fonda's name does evoke certain memories with me, and I must say that she is not my favorite American, but I also believe that, as odious as it was, Ms. Fonda acted within her constitutional rights," said McCain, a prisoner of war in Vietnam for 5½ years. "And to somehow say that someone who disagrees with American policy and even may demonstrate against it is somehow a member of an organization which makes that individual an enemy combatant is simply false. It is simply false."
Brennan replaces Michael Morell, the CIA's deputy director who has been acting director since David Petraeus resigned in November after acknowledging an affair with his biographer.
The Associated Press contributed to this report.