The contract runs until 2030.
Rodri was named the tournament's best player when Spain won World Cup gold this summer.
The 30-year-old left Atlético Madrid in 2019 and has since played for Manchester City. At the English club, the midfielder won several league titles, the FA Cup and the Champions League in 2023. The following year, he was awarded the Ballon d'Or, the award for the world's best footballer.
Barcelona is reported to be paying up to 840 million kronor, including bonuses, for the Spaniard.
