Rapid finished sixth in the Romanian top flight following their final match on Sunday.
Lennon, who recently came close to becoming manager of Republic of Ireland, returns to coaching after an 18-month hiatus. The 52-year-old led Omonia Nicosia to Cypriot Cup success in 2022 and then the Europa League group stage.
Besides Celtic, who he led to five Scottish titles across two spells in the dug-out, the former Leicester City, Celtic and Northern Ireland midfielder also managed Bolton and Hibernian.
Quoted on Rapid's website, Lennon said: "I hope to create a strong connection between myself and the fans, but that comes with getting positive results and performing. It is my responsibility. I know they are very passionate supporters who love the club. They are similar to Celtic fans."
Co-owner Dan Sucu believes the arrival of Lennon will bring new discipline to the team.
"He comes from a soccer culture, the Anglo-Saxon one, based on seriousness, work, success. A culture where decisions, once made, are no longer commented on or negotiated, but simply implemented.
"A coach with exceptional results, experienced but still young, energetic, very authoritative, a true leader.
"I am convinced that we will no longer have players who demonstrate their speed at three in the morning from the disco or on the ski slopes, or who show up to the team with extra pounds than the optimal weight."
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