The 36-year-old has agreed a free transfer to Elland Road following his departure from fellow Championship club Queens Park Rangers in May.
Green, capped 12 times by England, was among a crop of players released by QPR at the end of last season.
A former West Ham and Norwich keeper, Green spent four years with QPR and made more than 100 league appearances for the West London club.
His career appearances total almost 600 but he played no part in the second half of QPR’s recent Championship term and was surplus to requirements under Jimmy Floyd Hasselbaink.
QPR avoided playing him in an effort to prevent Green activating a clause which would have extended his contract beyond 2016 had he played 30 times last season.
United head coach Garry Monk, however, has been targeting a keeper with substantial experience of the English leagues to replace Marco Silvestri.
Silvestri has been first choice at Elland Road for the past two seasons but has struggled in patches and Green’s arrival casts doubt over his future.
Green said: “This is one of those opportunities where the first phone call asking if you want to come and play for Leeds is a very quick one. It was a ‘yes’ straightaway.
“I’m thrilled to be here. I’ve spoken to the manager and I know what he’s planning. What he said really resonated with me.
“After a long wait over the summer, the last few days have happened very quickly and now I’m ready to go.”
Goalkeeper Ross Turnbull is on their books for another 12 months.
Turnbull is fit again after breaking an ankle last October and is part of Leeds’ pre-season training camp in Ireland.
Green will now join up with Monk and his squad ahead of next week’s friendlies against Shelbourne and Shamrock Rovers.