Keane, who played for clubs such as Liverpool and Tottenham Hotspur with whom he won the League Cup in 2008, will leave on Tuesday for Ferencvaros' training camp in Spain.
"We announce the successor to Dutchman Pascal Jansen to lead our 35-time champion and 24-time cup winner team, as the 146-time national team player of the Republic of Ireland Robbie Keane has signed on Monday," the club said in a statement.
Keane was appointed player-manager of Atletico de Kolkata in India in 2018 but he took over his first head coaching role with Maccabi Tel Aviv in the Israeli Premier League in 2023.
Keane earned 146 caps with Ireland, the most of any player, and is still the country's top goalscorer with 68.
During his playing career, he scored more than 300 goals for Spurs, Leeds United, Liverpool, and West Ham United, among others.