The 28-year-old arrives on a free transfer after his contract with Lyon expired.
"Swansea City is pleased to announce the signing of French international striker Bafetimbi Gomis, subject to international clearance," read a statement on the club's website.
"The 28-year-old has signed a four-year contract with the Swans on a free transfer from French club Lyon."
Gomis was a target for the Swans last summer but after the proposed transfer stalled, they turned instead to Wilfried Bony.
Bony has been linked with a summer move away from the Liberty Stadium but Swansea have indicated that Gomis has been signed to play alongside the Ivorian, rather than in place of him.
Gomis scored 22 goals last season and 62 in total over 172 appearances but was left out of France's World Cup squad by Didier Deschamps.
He had also been a long-term target for Newcastle but talks between the Magpies and the player's representatives failed to yield a deal.
"I've been really impressed speaking with the manager and the chairman over the last few days," Gomis later told the club's website. "They showed they really wanted me - and that's one of the main reasons I chose Swansea ahead of the other interested clubs.
"They've been trying for over a year to sign me. It didn't quite happen back then, but they kept trying and I'm absolutely delighted to be here now.
"Although I've been aware of Swansea for a number of seasons, I've been following them a lot closer since the interest first materialised last year.
"It's a proud club with strong philosophies. It is growing all the time and I'm honoured to be given the opportunity to be part of it.
"I watched a number of games last season and I think the style will suit me. It's a collective, passing approach which I like. I think the way the team play creates lots of chances for the striker and hopefully I can score plenty of goals."
The Frenchman added that he was looking forward to forming a partnership with Bony.
"I do not see Wilfried Bony as competition, more of an association, because I know we can also play perfectly together," he said "We can benefit each other and that will be strong for the team."
Think that this could spell trouble for Swansea if the contract is as big as has been bundled about in the press.- dannyjohnson