The former Rangers captain ended an 11-year spell at Ibrox and will now reunite with ex-teammate Kenny Miller, who is head coach of the Israeli club.
Tavernier described the transfer as an honour and welcomed the chance to experience a new country and football environment.
"It’s a real honour to join a club with such a rich history as Maccabi Tel Aviv,” he said.
“Coming to a new country and experiencing a different environment is something I’ve always wanted to do in my career, so there’s a real excitement about the opportunity and the challenge ahead.
"Maccabi is a club that wants to win and compete for trophies, and that’s exactly what you want as a player. The aim is to give everything for the club, and I can’t wait to get started."
The 33-year-old is also excited by Maccabi’s ambitions to compete for trophies and is determined to give his best for the club.
His arrival adds experience and leadership to a Maccabi side hoping to challenge for domestic and European honours this season.