The 19-year-old Senegalese right back becomes the club's fifth signing of the summer following the arrivals of Arturo Vidal, Arthur, Clement Lenglet and Malcom after the successful completion of his medical.
Wague is expected to initially feature for the club's B team next season, but he is to train with the senior squad in the hope that over time he will pose as a significant threat to Nelson Semedo in the starting eleven.
The Senegal international is expected to put pen to paper on his deal at Camp Nou over the coming days, with his first training session with his new teammates set to take place on Saturday morning.
Moussa wagué is a topppp rb talent man. He was unreal at the WC. Great signing— J.R (@ElaficionadoFC) August 2, 2018
Wague played a combined 23 games for KAS Eupen in domestic competitions over the past two seasons, with a further 17 appearances coming in the form of Europa League play-off matches.
Despite his young age, the right back has already earned 12 caps for Senegal at the senior level, where his call up to the World Cup side resulted in a goal against Japan in the group stage, which made him the youngest African goalscorer in the competitions history.
Wague's arrival ensures Ernesto Valverde has plenty of options at his disposal for the right side of his defence, with senior options including Semedo and Sergi Roberto and Sergi Palencia also emerging from the B team.
However, Roberto is likely to see a shift back to midfield as a result of this deal - a position he has been deployed throughout pre season to offer support for Sergio Busquets.