The Uruguay defender has made just 24 appearances for Liverpool since his 2011 move from Nacional and spent the second half of last season on loan at his former club.
Coates has now been given the opportunity to play more regularly in the Premier League and the 23-year-old is keen to impress new manager Gus Poyet.
“It is a pleasure for me to be here and I am really excited for the opportunity to be part of Sunderland’s team," Coates told the club's official website.
“It has been great since I arrived here; I know the team and the manager now so it is really good.”
The centre-half, who featured once for Uruguay at the World Cup in Brazil, is looking forward to playing for his compatriot Poyet.
He added: “He was really good for Uruguay and he was a great player, as a manager he keeps improving after starting with Brighton where he did really well.
“For me it is really important to be here, he spoke with me and I know what he wants from me which is also important.
“He tries to play good football and that is really important for me because at Liverpool it was the same style.”