The 24-year-old, who joined the Tigers on loan in September last year, has now signed a two-and-a-half year deal at the KCOM Stadium.
Henriksen, a Norway international, has already made 11 Premier League and three EFL Cup appearances for the Humberside club.
He is quoted by Sky Sports News as saying: "It feels very good. I have a very good feeling about this club and this place.
"My first month here brought a lot of new things for me - new club, new teammates, new house, new baby - but now it all feels good because I know the move has become permanent.
"I now want to show my qualities on the pitch. The Premier League is many steps up from the football I have previously played. My form has been up and down so far, but hopefully I can show everybody my best."