"It's been an honor to share goals and dreams with my friend Keylor Navasin this competition, as well as with the rest of all my teammates, technical staff and our wonderful supporters," Rico said on social media.
"On 1 September last year, I arrived at PSG and I would never have imagined meeting a family like this. A family of teammates, of friends who have fought to the end to write the history of this club.
"Finally it couldn't be, we couldn't go back to Paris with the Champions Cup but I'm sure this group will fight hard to reach another final soon."
The 26-year-old, twice a Europa League winner with Sevilla who also spent a season on loan at Fulham, touched down in the French capital from the southern Spanish club on a temporary deal with an option to buy.
But he only played 10 matches for PSG, notably coming on as a replacement in the 2-1 Champions League quarter-final win over Atalanta and then starting the 3-0 semi-final victory over RB Leipzig which Navas sat out injured.