The France international becomes Garry Monk's second summer capture as he puts pen to paper on a four-year deal after failing to agree a new contract with Lyon
France international Gomis, who has previously been linked with a raft of Premier League sides, including Newcastle and Sunderland, has agreed a four-year deal with the Welsh outfit after leaving Lyon.
The 28-year-old scored 56 goals in 120 Ligue 1 starts for his former side and becomes Garry Monk's second signing ahead of the 2014-15 season following goalkeeper Lukasz Fabianski, who joined from Arsenal.
Gomis has surpassed 20 league goals in each of his last two seasons, with his form leading to 12 international caps.
He missed out on a place in Didier Deschamps's World Cup squad and instead travelled to Wales to complete a medical on Friday.
Gomis will battle with 2013-14 top goalscorer Wilfried Bony for a place in the starting line-up, while Michu also remains at the Liberty Stadium despite reports of interest from around Europe.