The 20-year-old, who was born in France to Algerian parents, will spend next season in Greece after failing to make his mark at St James' Park.
A statement on the Greek club's official website said: "Panathinaikos FC announces that it has entered into an agreement with Newcastle United for the one-year loan of Algerian international footballer Mehdi Abeid.''
Abeid joined the Magpies from Lens in July 2011 and was handed a senior competitive debut in a Carling Cup fourth-round victory at Nottingham Forest in September of the same year.
However, having made only three first-team appearances during the first half of last season, he was sent on loan to Scottish side St Johnstone in January with manager Alan Pardew admitting some of his young players had not developed as he would have liked.