The 23-year-old has been unable to establish himself at Anfield since joining from Nacional but becomes Gus Poyet's eighth recruitment of the transfer window on deadline day
The 23-year-old is Gus Poyet's eighth signing this summer.
Having joined the Reds in 2011, the youngster has been unable to break through into Brendan Rodgers's first team and was sent back to former club Nacional on loan last term.
Coates has 15 caps for Uruguay to his name and links up with compatriot Gus Poyet at the Stadium of Light after a summer in which he made a brief appearance at the World Cup.
He joins Billy Jones, Jordi Gomez, Costel Pantilimon, Jack Rodwell, Patrick van Aanholt, Will Buckley and Santiago Vergini in signing for the Black Cats this summer.