Saul joined Chelsea on a one-year loan deal during last summer's transfer deadline day but failed to adjust to the intensity of the English Premier League.
The 27-year-old endured a chastening debut against Aston Villa in September, when he was taken off at half-time and he failed to recover thereafter.
Saul made just 10 top flight appearances and 23 across all competitions, scoring one goal.
Chelsea had the option to make Saul's move permanent at the end of the campaign for £30m but they have declined and the Spain international will return to his parent club for next season.
A statement posted across Saul's social channels read: "Hello blues, I'm writing to take my leave of you. I would like to tell you how I felt during this adventure. Things didn't start well at all. After a long time at home, changing everything wasn't easy. Little by little, things got better.
"Everything in life serves to improve and learn, and that's what I take from this adventure. I'd like to thank the club for trying to take care of every detail to make me feel at home. I'd also like to give recognition to each worker, thank you. Thank you for making this club much bigger.
"Thanks to all the fans for supporting me through thick and thin. I will be forever grateful. Thanks to all the staff for making it possible for me to win titles with the blue shirt.
"But above all, I wanted to thank my teammates. They have been fundamental so that I wouldn't fall apart. They helped me to continue supporting the team and live a calm and positive day to day. Thank you."
