The 19-year-old, who has already earned five caps with England Under-21s, has signed a three-year deal with the option of a further 12 months in Albion`s favour.
Mattock can also play left midfield but he will predominantly be competing with Marek Cech for the left-back slot following Paul Robinson`s departure to Bolton.
Boss Roberto Di Matteo said: "Joe is exactly the kind of player we're looking for. He's a young, talented, English left-back who's got plenty of Championship experience despite his young years.
"Joe is hungry for success and he was very keen to join us. He's a quick, solid defender with a very good left foot."