Mendes joins fellow Brazilian Jean Lucas at the club after Ndombele became Tottenham's record signing on Tuesday, joining the Premier League team for a fee that could rise to €70 million (£63m/$79m).
Lyon and Lille have not revealed the terms of Mendes' transfer, though he is reported to have cost around €25m (£22m/$28m).
Thiago Mendes s'engage avec l'Olympique Lyonnais !— Olympique Lyonnais (@OL) July 3, 2019
He becomes Lyon's third signing ahead of the 2019-20 campaign, following on from the arrivals of Jean Lucas and Romania goalkeeper Ciprian Tatarusanu.
However, the Ligue 1 side have lost Ndombele to Spurs and also left-back Ferland Mendy to Real Madrid, while Nabil Fekir continues to be linked with an exit.
The Gunners have apparently made initial contact over signing the 25-year-old as Unai Emery looks to improve his squad after failing to secure Champions League qualification last season.
Lyon, under Bruno Genesio's successor as head coach Sylvinho, open the new season away to Monaco next month before hosting Angers in their first home game.
0/10 - Since Thiago Mendes’ first game in Ligue 1 in 2017/18, Lille never won a game in the top-flight without the Brazilian midfielder (0/10, D4 L6). Loss. pic.twitter.com/iJS1N0Zr2T— OptaJean (@OptaJean) July 3, 2019