The 27-year-old cost the Blues £4.5m to loan from the Spanish champions last summer, but he endured a nightmare stint in the English capital under Thomas Tuchel.
Saul only managed one goal in 23 appearances for Chelsea in all competitions, with that solitary strike coming in an FA Cup fifth-round success over Luton Town.
The Spaniard would establish himself as a regular starter in cup tournaments, but he only made a total of 10 appearances in the Premier League over the course of the 2021-22 season.
Five of Saul's 10 top-flight games came from the first whistle, while he was only named in the first XI once in the Champions League - playing 75 minutes of Chelsea's final group-stage match with Zenit St-Petersburg.
Chelsea possessed the option to make Saul's stay a permanent one for €35m (£29.8m) at the end of the season, but the Blues have already informed Atletico that they will not be triggering that clause.
Saul took to social media on Tuesday night to confirm that his time at Stamford Bridge was over, and the Spaniard hopes to "improve and learn" from his tough year in England.
"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," Saul wrote on Twitter.
"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! @ChelseaFC."
Saul returns to the Wanda Metropolitano to reunite with Diego Simeone and Atletico before deciding on his next career move, and his Rojiblancos deal still has four years left to run.
The Spaniard has amassed 43 goals and 20 assists in 340 appearances for Atletico since joining from Real Madrid's youth academy in 2008 and was strongly linked with a move to Manchester United before his difficult spell at Chelsea.
Chelsea boss Tuchel is expected to be in the market for a new midfielder following Saul's exit, with Jorginho and N'Golo Kante also facing uncertain futures in West London.
The Blues are said to have joined the race to bring Leeds United's Kalvin Phillips to the club but have been forced to concede defeat in their pursuit of Aurelien Tchouameni, who is on the brink of signing for Real Madrid.