The 22-year-old started his career at Sevilla, who he memorably helped qualify for the Champions League with a late winning goal in the final match of the 2009-10 season.
A move to the Blaugrana followed last summer, and he has since continued to development for Barcelona B, before agreeing to join the Championship side to further his progression.
Rodri told the club's official website: "I am very happy to be here and I can't wait to get started.
"I was at the game on Saturday [a 2-2 draw at Derby] 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.
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"That was an away game for the club so I can’t wait to see them in a home game."
The forward made 35 appearances for the Barcelona B side last season in the Segunda Division, scoring seven goals, and has two caps for the Spain under-21 side.
He continued: "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.
"I come here with a lot of excitement and I want to start as soon as possible."