The Senate action followed approval earlier in the day by the Senate Foreign Relations Committee, which Kerry formerly led.
The Senate voted 94-3 in favor of Kerry, who was his party's failed presidential nominee in 2004. Republicans James Inhofe of Oklahoma and Ted Cruz and John Cornyn of Texas voted against the nomination.
Sen. Robert Menendez, D-N.J., cited Kerry's extensive experience with foreign leaders in supporting the nomination, Roll Call reported.
"I can think of no one better prepared to take on the challenges of this position," Menendez said.
Sen. Bob Corker, R-Tenn., said Kerry had been preparing for the job since his father was a diplomat.
"I'm honored beyond words," Kerry said following the vote.
Kerry, who has been in the Senate for three decades, told reporters after the vote he was "wistful" about leaving the Senate.
During his confirmation hearing last week, Kerry testified the United States must be smart about how it handles the world's hot spots.
"We cannot afford a diplomacy that is defined by troops or drones or confrontation. We have to find a diplomacy that achieves ... understanding, rapprochement, whatever you want to call it," he said.
The Hill said the approval never was in doubt, given that Republicans had urged President Barack Obama to nominate Kerry instead of U.N. Ambassador Susan Rice, who ran into opposition for voicing what turned out to be a false analysis of the events at a State Department mission in Benghazi, Libya, that left four Americans, including Ambassador Christopher Stevens, dead.
The White House released a statement in which Obama said he was "pleased that the Senate has confirmed John Kerry as our next secretary of state with overwhelming bipartisan support."
"John has earned the respect of leaders around the world and the confidence of Democrats and Republicans in the Senate, and I am confident he will make an extraordinary secretary of state," Obama said. "I look forward to his counsel and partnership in the years ahead as we ensure American leadership in the world and advance the interests and values that keep our nation strong."
Clinton's last day as secretary is Friday.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Couple mistakenly served bag of cash at McDonald's drive-thru