The councillor for Splott will take over from Phil Bale who has led Wales' biggest local authority since 2014.
Labour retained control of the council in elections last week, but years of infighting convinced some members a new leader was needed.
Mr Thomas, 31, was one of five candidates who put their name forward to challenge Mr Bale.
Lynda Thorne, Ed Stubbs, Graham Hinchey and Chris Weaver were understood to be the other candidates.
Mr Bale was elected leader of the council's ruling Labour group in March 2014, after Heather Joyce stepped down.
In May 2015 he survived a challenge to his leadership from Ms Thorne, who he had defeated the previous year.
Despite the internal strife, Labour retained its majority hold on Cardiff council, although it won six fewer seats than in 2012.
The Conservatives overtook the Liberal Democrats to become the official opposition with 20 seats.
The Tory group have also chosen a new leader after David Walker stood down from the position.
Mr Walker has been replaced by Rhiwbina and Pantmawr councillor Adrian Robson.
Labour councillors in Cardiff have chosen Huw Thomas to be their new leader.