The 32-year-old will leave along with loan pair Loic Remy and Luuk de Jong who will return to respective parent clubs QPR and Borussia Monchengladbach.
Speaking about Ameobi's departure, Alan Pardew said: "I would like to thank each of these players for the effort, attitude and application they have put in while at the Club.
"However, I have to make a special mention of Shola Ameobi, who has been an incredible servant to Newcastle United.
"Such loyalty and commitment in the modern game is rare and Shola was not just a great player on the pitch but a key figure off it too."
Ameobi scored 79 goals in 379 appearances for the Magpies.
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