Gomis has signed a four-year deal at the Liberty Stadium, and Monk, who was installed as the club's permanent manager at the end of the last campaign, has described the transfer as a "very big and important signing".
The 35-year-old told the club's official website: "You are talking about a quality striker who has played international, Champions League and top-flight football in France for a big club.
"I'm very happy. It's a fantastic signing; a very big and important signing for the club. It shows just how far we have come that we can attract a player of his quality."
Gomis netted 17 goals in 43 appearances for Lyon last season.