Gomis, capped 12 times by France, has frequently been linked with a move to the Premier League in recent years.
And he will now continue his career at the Liberty Stadium after turning down the opportunity to extend his association with Lyon.
The 28-year-old arrives in south Wales having scored 10 goals or more in eight successive Ligue 1 seasons.
After initially impressing for Saint-Etienne, Gomis moved to Lyon in July 2009 and has continued to find the net on a regular basis.
He managed 14 goals in 33 league appearances last season and Swansea claim to have beaten a host of fellow Premier League clubs to the forward's signature.
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