The former Chelsea and Manchester United man had only arrived at Rennes from Roma in the most recent summer transfer window and made 19 appearances for the club in the first half of the season.
Matic registered three assists for Julien Stephan's side during the group stage of the Europa League and started 11 Ligue 1 matches, but he was removed from the first-team picture in acrimonious circumstances just before Christmas.
The Serbian's frustrations stemmed from broken promises made by the club when he signed for them relating to his children's education, having supposedly been told that they would be enrolled into an international school, although no such establishment exits in Rennes.
There was no resolution to the stand-off in the weeks that followed, and Matic was spotted heading out of Rennes with his family, although he soon took to Instagram to admit responsibility for the education farce.
The 35-year-old confirmed that he would soon return to Roazhon Park to enter talks with the club after solving the "big problem", but Rennes subsequently released a scathing statement accusing the midfielder of missing several training sessions.
Les Rouges et Noir labelled Matic's behaviour "totally incomprehensible", and the veteran midfielder handed in a transfer request to the club, who were happy to grant him a move elsewhere.
Rennes were reportedly hoping to offload Matic to a club outside of Ligue 1 amid rumours of interest from Italian and English teams, but Lyon have won the race for the Serbian's signature.
Les Gones have confirmed that they have paid €2.6m (£2.2m) to sign the former Serbia international, who has committed his future to Pierre Sage's side until the summer of 2026.
Upon his arrival at the Groupama Stadium, a statement from Lyon read: "Olympique Lyonnais is delighted to have successfully attracted such a charismatic and experienced player as Nemanja Matic to the club."
During the prime of his career, Matic won three Premier League titles with Chelsea and spent five years on the books with Manchester United from 2017 to 2022, before leaving Old Trafford to join Roma on a free transfer.
In his only season with the Giallorossi, Matic started 13 Europa League matches to help Jose Mourinho's side reach the final, where they were beaten on penalties by perennial winners Sevilla.
Lyon sit 16th in the Ligue 1 table owing to a horror start to the season, and Matic could make his Gones debut at home to Marseille on February 4.