The Uruguay international was sold by Liverpool last week for €60m.
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And Nunez posted to social media yesterday: "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 my staff and teammates - thank you, and all the very best for the future."
Nunez struck on debut, as a second-half substitute, on Sunday in Al-Hilal's 6-0 preseason friendly win against FC Aarhus.