The 28-year-old replaces the retired Jamie Carragher as deputy to Steven Gerrard after making 209 appearances for Liverpool since joining from Brondby in 2006.
Reds manager Brendan Rodgers told LFC TV: "The job of the captain and vice-captain here at Liverpool is very, very important. I wanted to give myself time over the course of the pre-season to assess a number of the players and obviously Daniel was one of them.
"His loyalty and his passion for Liverpool is second to none. And if you add that on to his footballing qualities, then I think it's a good choice for everybody."
Agger, who has scored 12 goals for the Anfield club, played in the 2007 Champions League final and helped the Reds win the 2012 League Cup before signing a new long-term contract last October.