Posting his farewell on social media, Nunez said: "Thank you, Liverpool.
"Three years on, it's time to say goodbye. I'll take with me countless memories that will live with me forever. I leave with a full heart, thanks to the love of a crowd that never let me down and always had my back - through the highs and through the lows.
"Liverpool will always be part of who I am. I'll miss you more than words can say. To all the staff and my teammates - thank you, and all the very best for the future."