Keane was recently part of Sam Allardyce's coaching set up that unsuccessfully tried to keep Leeds United in the Premier League.
The 42-year-old is going into his first full-time managerial position since serving as player-manager at Indian side ATK in 2018.
Keane will come in as a replacement for Aitor Karanka, who departed the club earlier this month.
Maccabi Tel Aviv are Israel's most successful club, having won the championship 23 times in their history but finished third last season.
Keane told the club website: “I am delighted to take on this challenge at Maccabi. My team and I look forward to beginning work and we have confidence in our ability to do what is necessary to prepare the team for the coming season.”
The club’s owner, Mitch Goldhar, said: “Robbie brings the mentality, character, energy and focus of a winner, traits he exhibited everywhere he played.
“These characteristics now combined with ambitions to succeed as a coach are aligned with our objectives at Maccabi.”
Keane is the record goalscorer for the Republic of Ireland with 68 goals in 146 appearances.
He also turned out for Inter Milan, Liverpool, Wolverhampton Wanderers and LA Galaxy during his playing career.
