The duo, who will face each other in the Merseyside derby this weekend, will appear in adverts for the network and contribute to programmes next season.
Fellaini said: "It's exciting to be involved with BT Sport and I am looking forward to contributing to the programmes next season. I hope that I can bring some real insight from a player's point of view.
Sturridge added: "These are exciting times for me. I feel that I have settled in well at Liverpool and next season I want to reach new levels on and off the pitch. I am looking forward to being involved in the BT Sport ads and giving the viewers some fresh insight into the game."
BT Sport will have the rights to games from the Premier League, Serie A and Bundesliga, as well as NASCAR, Aviva Premiership rugby and WTA matches.