The 32-year-old was expected to leave the club, which he first joined as a youth back in 1995, after both parties decided against agreeing fresh terms.
The forward, who has recently been linked with a move to Hull City, scored 79 goals in 397 appearances for the Magpies.
"Following discussions with Newcastle United, both parties felt it was the right time for us to part company," Ameobi told the club's official website. "I've been at Newcastle United all my career and I've enjoyed every moment and always worn the famous shirt with pride. I am now looking forward to starting a new chapter in my career.
"I would like to place on record a big thank you to everyone at Newcastle United. I wish the club great success in the future and I'm sure with the team and management they have, Newcastle United will go from strength to strength.
"Finally, a big thank you to the supporters who have always been fantastic. I hope to come back to Newcastle United one day in some capacity to help repay some of the faith and loyalty that everybody connected to the club has shown me during my time here."
Manager Alan Pardew added: "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. He is a leader of men, a great role model for our younger players and I wish him well for the remainder of his career."