With 99 percent of the ballots counted Wednesday, Klobuchar had 58 percent of the vote compared to 38 percent for Kennedy, a congressman from Minnesota's Sixth District.
"Today you had the chance to raise your voice for change and you did it," Klobuchar told supporters at a St. Paul hotel.
Kennedy conceded less than three hours after the polls closed Tuesday evening, the Minneapolis Star-Tribune reported. He said this was "not our year."
McPhee, Cokas 'working on their marriage' after affair
Attkisson leaves CBS News, reportedly over network's 'liberal bias'