Carrico only joined Reading in January on a contract until 2015 from Sporting Lisbon, but he struggled to make an impact at the Madejski Stadium.
He made just three appearances en route to Reading's relegation from the Premier League and he is now being allowed to move on by manager Nigel Adkins.
The 24-year-old, who can play in midfield and defence, acknowledged last week that he is keen to leave Reading and would relish the opportunity to join Sevilla.
"Sevilla is a great club," said Carrico. "I would love to play for them. I will not be staying at Reading."
The Spanish side have also confirmed that Carrico is on his way to the club after they had also been interested in a deal in January.