The midfielder will join Atletico at the end of this season, reports Marca.
The 21 year-old is a former Atletico junior, but was released due to physical concerns. However, now standing at 1.9m, Rodri is set to return next season.
Barcelona expressed interest in Rodri in recent days before learning of the Atleti deal.
Atletico will pay €20m up front for the midfielder with another €5m due in bonuses.