The 22-year-old, who has scored eight goals in 35 games for Barcelona's B team, said that he is excited to join the Championship club.
Rodri told the club's official website: "I am very happy to be here and I can't wait to get started.
"I come here with a lot of excitement and I want to start as soon as possible.
"I am a striker and I am confident I will get a lot of chances and confident I can score goals to help the club."
Rodri is expected to be in the club's squad to face Birmingham City on Tuesday night.