The 16 year-old will play for the Juvenil A side (U19s).
Luzzi has signed a three-year deal at Camp Nou with the option to extend it by an additional two years and was presented at the weekend alongside Xavier Vilajoana and Patrick Kluivert.
The teenager is a quick, agile player that knows where the net is. He has been the top scorer at every age group at Rayo, where he's developed over the years. He has been training with the club's first team since he was 15.