The 63-year-old, who parted company with Liverpool five weeks ago after an ill-fated six-month stint at Anfield, succeeds Roberto di Matteo in the Albion hotseat.
Di Matteo was relieved of his duties and placed on gardening leave on Sunday following a 3-0 defeat to Manchester City - the Baggies' 13th defeat in 18 games in all competitions.
WBA statement: "West Bromwich Albion are delighted to announce they have appointed Roy Hodgson as the club's new head coach.
"The 63-year-old former Inter Milan, Switzerland, Fulham and Liverpool boss has this morning committed himself to the club until June 2012.
"Hodgson was voted manager of the year by the League Managers' Association last season after guiding Fulham to the Europa League final.
"Michael Appleton, who was appointed caretaker head coach on Sunday after Roberto Di Matteo was relieved of his duties, will remain in charge for the West Ham game.
"The club are now channelling all of their efforts into supporting Appleton, his assistants Keith Downing and Dean Kiely and the players as they prepare for tomorrow's vital game."