The 48-year-old Scot has signed a two-year deal at the Hawthorns to take over from England manager Roy Hodgson.
Steve Clarke: "I'm absolutely delighted to be given this opportunity.
"Becoming a head coach in my own right has always been an ambition of mine and I feel I have served my apprenticeship.
"I've done everything I could as an assistant.
"I'm delighted West Bromwich Albion have given me the chance to make that progression and I'm determined to make the most of it."