A winger who can also play in defence, the 6 feet 2 inch tall 28 year old has rejected loan opportunities in England to try his luck in the SPL.
Caley Jags gaffer Terry Butcher says: "I have been tracking Claude for a good number of years, but never managed to get him so we're very pleased that he has flown north and put pen to paper.
"He's big, strong and pacy and can score goals, so he will be a very exciting asset to the Club. Claude joins Kenny Gillet and Gregory Tade to give us a triple French influence in our squad.
"Having already landed striker Sam Winnall from Wolves on loan, it gives us more depth in a pool which has continuously been depleted by serious injuries."
Gnakpa joined Luton Town from Peterborough United in the summer of 2008 and he fired 22 goals in 107 appearances for The Hatters. This included scoring the winning goal in Luton's 2009 Football League Trophy final triumph when he struck five minutes into extra time to give his side a 3-2 win over Scunthorpe United at Wembley Stadium.