The 22-year-old former Spain Under-21 international - full name Rodrigo Rios Lozano - has joined the Owls on a season-long deal.
Rodri said: "I am very happy to be here and I can't wait to get started.
"I was at the game on Saturday and I thought the team did very well in the second half, the fans on a scale of 0-10 were definitely a 10. It was a massive crowd that came from Sheffield.
"That was an away game for the club so I can't wait to see them in a home game. I come here with a lot of excitement and I want to start as soon as possible.
"Everyone knows the standard of player at Barcelona, but in the Barcelona B side, it is full of players with much potential - very talented guys.
"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, allocated the number 15 shirt at Hillsborough, began his career at Sevilla before moving to Barcelona, where he made 35 appearances and scored eight goals for the B side.