The nominee spent weeks reaching out to members of the Senate, meeting individually with lawmakers to address their concerns and seeking to reassure them about his policies.
Hagel's inconsistent performance during some eight hours of testimony during his confirmation hearing last month undercut his cause.
On Feb. 12, the Armed Services Committee approved the nomination on a party-line vote of 14-11. Two days later, a Democratic move to vote on the nomination fell a few votes short as Republicans insisted they needed more time to consider the pick.
Hagel's nomination also became entangled in Republican demands for more information about the deadly assault on the U.S. diplomatic mission in Benghazi, Libya, last September. Ambassador Chris Stevens and three other Americans were killed in that attack.
Republicans allowed the nomination to move forward, with 18 Republicans joining the Democrats. Many had warned against the precedent of denying a president his Cabinet choices.
Paul's vote for Hagel came as something of a surprise. Moira Bagley, a spokeswoman for the senator, said that while he disagrees with Hagel on a number of issues, Paul believes a president should have some leeway in his political appointments.
Missing the vote was Democratic Sen. Frank Lautenberg of New Jersey.