The No.26 takes up the role of deputy to Reds skipper Virgil van Dijk in his ninth season with the club.
Robertson, who wears the captain’s armband for Scotland at international level, replaces Trent Alexander-Arnold in the position after his departure to Real Madrid in June.
Asked for an update on the vice-captaincy on Friday, Slot told reporters: “It’s Robbo.
“He has played here so many years, won the league twice. It was Virgil, Trent, Robbo and Mo [Salah] last season. Trent left, so there are a lot of logical reasons for [the decision].
“He is a very good player, plays many games, knows what it takes, knows the culture, but also knows the culture of the club and the dressing room.
“Apart from all the quality he shows on the pitch, he plays also a big role in the culture we have here at this club. Which is, [as] I said many times last season, the biggest gift I could get from Jürgen [Klopp].
“That’s also something we definitely have to keep for my successor to have, this same culture, if I am ever leaving this club.”
In becoming a two-time Premier League champion with Liverpool, Robertson has made 344 competitive appearances since arriving at the club from Hull City in 2017.
Along the way he has also claimed winner’s medals in the Champions League, FIFA Club World Cup, FA Cup, Carabao Cup (twice) and UEFA Super Cup.
He has captained the Reds on seven occasions to date.
