Sinisterra, 24, has made 17 appearances for the Cherries after joining them in September, scoring three goals.
On signing permanently for Andoni Iraola's side, the Colombian said: "I’m really happy to make this move. I’m excited to play for Bournemouth for the long term.
"I feel really comfortable here and the fans are really nice. When I meet them in the streets, they show the love.
"I’m really happy here and I’ve settled really well; I’m looking forward to the rest of the season."
Bournemouth are 12th in the Premier League and face Fulham on Saturday.