"I am happy to take on this challenge at Maccabi," Keane told the club website.
"My team and I are already looking forward to starting work and we are confident in our ability to do what is necessary to prepare."
Keane earned 146 caps with Ireland, the most of any player, and is still the country's top goalscorer on 68. In May he joined the coaching staff of Leeds United as an assistant coach following the appointment of Sam Allardyce as manager.
Leeds lost three out of four games remaining in the season under Allardyce and were relegated, before the manager left the club by mutual agreement.
"Robbie brings with him the mentality, character, energy and focus of a winner, qualities that he demonstrated everywhere he played," Maccabi owner Mitch Goldhar said.
"These characteristics combined with the ambitions to succeed as a coach are in line with our goals at Maccabi."
Previously Keane was an assistant coach for the Ireland national team and Championship (English second tier) side Middlesbrough.
During his playing career, Keane scored more than 300 goals for Tottenham Hotspur, Leeds, Liverpool and West Ham United, among others.
Maccabi finished third in the 2022-23 Israeli Premier League season.
