The 23-year-old Uruguay international is Sunderland's eighth signing of the transfer window.
Coates has been capped 15 times by his country and joined Liverpool from Nacional in 2011.
He returned to Nacional in his homeland on loan last season after making 24 appearances and scoring twice for the Anfield club.
The Coates deal makes good on a pledge made by Sunderland coach Gus Poyet to add to his squad before the deadline.
Following Saturday’s 1-0 defeat to QPR, Poyet said: "We don't have enough [players]. We know the numbers I wanted to work with and the numbers we've got.
"I will be on the phone all the time [until the window closes]. I'm not a fan of the transfer window being open during the season, but I'm not going to complain. It's the same for everyone."
However, as Coates arrives another defender is leaving the Stadium of Light after Valentin Roberge joined Ligue 1 side Reims on loan until the end of the season.
The 27-year-old joined Sunderland a year ago from Portuguese outfit Maritimo and has played 13 times for the club.
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