Da Silva, 33, has agreed a two-year contract with the Ligue 1 giants, who confirmed the transfer on Wednesday.
The French midfielder spent three seasons with Rennes, where he won the Coupe de France in 2019 and, the following year, helped guide the club to its maiden Champions League appearance.
"It is a great point of pride for me to join Olympique Lyonnais," Da Silva said during his unveiling at the Groupama Stadium.
"I am aware I am becoming part of a very big club and I can't wait to wear these new colors.
"Today I visited the facilities, the stadium, I toured the museum and it really makes you want to be a part of an institution whose ambitions are very high and I'm happy as I think I can still improve here."
Lyon are currently managerless following the departure of Rudi Garcia at the end of the season.
Christophe Galtier, who stepped down as Lille coach after clinching the Ligue 1 title on Sunday, is rumored to be the top target to take the reins of Les Gones.