The 23-year old Dubliner, will compete will Estonian international Mart Poom and Kelvin Davis at the Stadium of Light in the Black Cats' first season back in the Premiership.
Murphy spent most of last season on loan at Walsall, making 25 appearances for the club in League One.
Murphy said: "I am very excited about the move. I didn't manage to force my way into Bryan Robson's plans at West Brom, but once I had an offer on the table from Sunderland, I didn't need to think about it.
"Sunderland is a huge club with a passionate set of fans and although I will have some stern competition from the other goalkeepers here, I know the experience will make me a better player.
"I really enjoyed getting some first-team football under my belt at Walsall last season, hopefully I can force my way into Mick McCarthy's ideas once the season gets underway."