The 25-year-old has played 23 times for his country, while he made 26 appearances for Napoli this past season.
Cajuste, who won a Danish Superliga title with FC Midtjylland earlier in his career, cannot wait to start in the Premier League.
"We're really happy to add Jens to the squad," said Ipswich boss Kieran McKenna.
"He gives us another different profile to our midfield and puts us in a strong position in that department.
"Jens has a lot of experience across top leagues in Europe and in international football. He brings good physical and technical qualities to the squad and he is a very dedicated and committed professional."
Cajuste welcomed the move, adding: "It took a little while with the negotiations but I'm finally here and I'm very excited.
"I've had great conversations with the manager and this seems like a very interesting project. It's an ambitious club and a team that is progressing."