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 is back at his parent club for next season.
"I'm looking forward to coming back home and I'm mentally at my best," Saul told the club's official website.
"I know that I come from a loan period in which I haven't had many minutes, and that I have to work hard, persevere and make a lot of sacrifice to get a place in the team.
"There is a very high level of competition; we have an enormously competitive team.
"I can only be grateful to all the people at Chelsea for their trust and to my team-mates for making the year so easy for me and helping me, and to Atleti for making it easier.
"I come with a lot of humility, thinking about working and helping the team in whatever way I can and from wherever I can.
"I really want to show that, despite having had a complicated year, it has been very good for me to improve and grow in many aspects, both sporting and personal."
