The Portuguese midfielder moved to England from Sporting Lisbon in January 2013, but struggled to make an impact as relegation out of the Premier League was suffered in his first season at the Madejski Stadium.
With Reading quickly deeming him surplus to requirements, Carrico was allowed to head for Spain on a season-long loan last summer.
He was to help Sevilla to a fifth-placed finish in the 2013/14 campaign, as well as Europa League glory following a thrilling penalty shoot-out victory over Benfica.
Carrico will now be remaining in Andalusia, with Reading having sanctioned a sale.
It is reported that a fee of around £1.5million has allowed Sevilla to secure the 25-year-old’s services.
Reading’s director of football Nick Hammond told the club’s official website: “We would like to wish Daniel all the very best.
“It’s a good deal for him and for Reading Football Club.
“He joined us last year at a difficult time for the team and when he was not up to full match fitness, but has gone to Spanish football, which has been great for him, and has done extremely well.
“He’s a fantastic individual and we wish him all the best at Sevilla.”