Clarke takes his first senior managerial role with Baggies chairman Jeremy Peace convinced the 48-year-old has the right qualities to replace new England head coach Roy Hodgson.
Norwich-bound Chris Hughton, who was interviewed initially for the post before Hodgson was appointed, and former Schalke 04 boss Ralf Rangnick were also in contention to take over from Hodgson.
But Clarke is the man chosen to replace Hodgson, and he will begin work only a couple of days after finalising the terms of the end of his spell at Liverpool as Kenny Dalglish's assistant.
Albion's sporting and technical director, Dan Ashworth, told the club's official website: "I'm delighted to welcome Steve to the club.
"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.
"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.
"After holding talks with Steve, he emerged as the outstanding candidate."
Clarke has gained plenty of experience working as number two at Newcastle, Chelsea, West Ham and most recently at Anfield under Dalglish.
He will have a hard act to follow in Hodgson who guided West Brom to a top 10 finish in the Premier League last season and ensured a third year of top flight football.
But he has worked under the likes of Jose Mourinho, Ruud Gullit, Sir Bobby Robson, Gianfranco Zola and most recently Dalglish and is one of the most respected coaches in the game.