Elneny joined Arsenal from Swiss side FC Basel in 2016 for 5 million pounds ($6 million) and has made 161 appearances for the London club.
A knee injury restricted the midfielder to eight outings during the 2022-23 season. He has made six appearances in all competitions in Arsenal's current campaign.
"Gooners, I'm here today to send you a message, to say goodbye and thank you for everything you've done for me," Elneny said in a video posted on X on Friday.
"The love, the support and the kindness. I'm really going to miss you so much and you'll be in my heart forever."
Elneny did not say where he would go after leaving Arsenal.
He said he would bid farewell to fans at the Emirates on Sunday as Arsenal host Everton in their final league match, hoping for a Manchester City slip-up against West Ham United to secure their first title in 20 years.
