A Sweden Under-21 international, Inoussa left his homeland to join Caen as a teenager and got his first taste of senior football with the French club.
He had loan spells with Real Murcia and Valencia's second-string side before returning to Sweden to play for Brommapojkarna in 2023.
Inoussa moved to Gothenburg-club Hacken last year and has since scored nine goals in 23 appearances and had been linked with a number of clubs including Celtic.
Swansea director of football, Richard Montague, said: "Zeidane gives us something different to what we've had this season. We hope that he's a player who will get fans off their seats.
"We're delighted to have completed this deal so early, and we believe it will help us to hit the ground running in August."
Inoussa will be joined in Wales this summer by fellow countryman Melker Widell, who agreed a move in the last transfer window.
Swansea are also lining up a move for Kilmarnock striker Bobby Wales.