The 26-year-old centre-back has signed a three-and-a-half-year deal after arriving on Wearside to finalise his move and undergo a medical.
Steve Bruce: "Matthew is a very talented defender and has been coveted by a number of top-flight clubs recently, so I'm very pleased to have brought him here.
"He will add to our options across the back ahead of some very important games. I'm sure he will prove to be a great signing for the club."