The 24-year-old passed a medical in Seville on Monday and joins the La Liga outfit with a view to making the move permanent.
Carrico arrived at Madejski Stadium from Sporting Lisbon in January but made only three appearances for the Royals in the Premier League last season.
A Royals statement read: "We would like to wish Daniel the very best of luck at Sevilla and thank him for his hard work and his professionalism during his six months at Reading Football Club."
- La Liga
- Sporting Lisbon