Washbrook and Talanoa have signed one-year extensions with last season's Challenge Cup winners, while Thompson will stay for another two terms at the Super League club.
"It's really pleasing to see all of them stay with the club," Hull head coach Lee Radford said.
"Having tasted success last year, I've no doubt they will be hungry for more."
Loose-forward Washbrook, 31, said: "It's a great club and I'm a Hull lad so it was an easy decision for me. We all want to carry on the success of last season."
Winger Talanoa added: "I'm really happy here and my family are settled. Now it's about building on the back of last season and getting our hands on more silverware."
And loose-forward Thompson said: "It's massive to have my future secured."
Danny Washbrook, Fetuli Talanoa and Jordan Thompson have all signed new deals at Hull FC.