The Egypt midfielder is departing as his contract expires at the end of next month.
Elneny said: "Gooners, I'm here today to send you a message, to say goodbye and thank you for everything you've done for me.
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"The love, the support and the kindness. I will truly miss you so much and you will be in my heart forever. I wanted to say how much I love you and how much you mean to me.
"I will never forget how you supported me."