"We firmly believe we have appointed the right man to keep the club moving forward," Albion's sporting and technical director Dan Ashworth said on the club's website.
"Steve has worked alongside and learned from some top managers and, most importantly, he knows the Premier League inside out and what it takes to succeed at this level.
"He is a talented British coach who has served his time in the trenches as a number two in order to get an opportunity to be in sole charge of a team - and we are delighted to give him that chance."
Clarke, who left Liverpool this month after Brendan Rodgers replaced Kenny Dalglish as manager at Anfield, has signed a two-year deal and takes over from Roy Hodgson at Albion.
Hodgson was named England manager in May.
"I'm absolutely delighted to be given this opportunity," said the 48-year-old Clarke, who has also served as assistant manager at Chelsea, Newcastle and West Ham.
"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.
"It's a process I've gone through, with a plan in mind to work as hard as I could alongside some of the best managers and coaches in the world, learning as much as possible from them, before stepping out on my own."
Clarke was appointed Liverpool first team coach on a three-year contract in January 2011 as Dalglish's first appointment on replacing Hodgson as manager.
As a player, Clarke made over 400 appearances for Chelsea and was Jose Mourinho's assistant at Stamford Bridge, winning two Premier League titles with the Portuguese.
"After Roy was appointed as England manager, we cast the net far and wide to identify the most suitable candidate to fill his shoes," Ashworth added.
"From the outset, we decided to pursue candidates who are renowned for their coaching ability and Steve was very much at the forefront of our thoughts because of the clubs he has worked at and the high regard he is held in within the game."
West Brom finished 10th in the Premier League last season.
