Clarke's coaching career
Newcastle United: 1998-1999
West Ham: 2008-2010
The 48-year-old left his role at Liverpool on Wednesday, where he was assistant manager before Kenny Dalglish’s dismissal in May.
"Becoming a head coach in my own right has always been an ambition of mine and I feel I have served my apprenticeship," Clarke said.
"I've done everything I could as an assistant. I'm absolutely delighted to be given this opportunity.”
"I'm delighted West Brom have given me the chance to make that progression and I'm determined to make the most of it."
Clarke's appointment ends West Brom's month-long search for a new boss after Roy Hodgson joined England.
Newly appointed Norwich boss Chris Hughton, former Chelsea manager Claudio Ranieri, Ray Wilkins and former Schalke boss Ralf Rangnick had also been linked with the role.
West Brom sporting and technical director Dan Ashworth revealed that Clarke's coaching ability was key to his being chosen.
He said: "We firmly believe we have appointed the right man to keep the club moving forward.
"After Roy was appointed as England manager we cast the net far and wide to identify the most suitable candidate to fill his shoes.