The 37 year-old joins David Wagner's side after having his contract at Elland Road mutually terminated, paving the way for a deal with Town until the end of the current 2017/18 campaign.
The former England international has made over 650 appearances during a 21-year career and was ever-present for the Whites last season but has struggled to make an impression on new head coach Thomas Christiansen this term.
Speaking on the deal, in which the club have the option of a further year's extension, David Wagner said: “I think it makes total sense to bring Rob Green in because after Jonas Lössl, who has done an excellent job so far, we have very young goalkeepers with Joel Coleman and Ryan Schofield.
“I have spoken to Paul Clements and we agreed that we wanted to add more experience to our goalkeeper group.
“I met Rob and he is a very experienced guy and a good guy. He knows the role I expect from him in the next 10 months he’ll be with us. I’m very happy he can join us.”