The 33-year-old, who has made 337 Super League appearances, debuted for Hull in 2005 and had two spells at KCOM Stadium either side of a stint with Wakefield Trinity.
Washbrook said: “I'm looking forward to the challenge of helping the club keep progressing the way they have under James [Ford's] leadership.
“Having spoken to a number of players, current and past, they spoke highly about all aspects of the club and that excited me.”
Ford, York's coach, said: “I’m very pleased to bring a player with such professionalism to the club.
"Danny has a wealth of experience that will help improve our culture further and directly impact on the younger players in the squad.
"He’s a very intelligent rugby player who will benefit all aspects of our performance. I’m looking forward to working with Danny.”