Former Nottingham Forest chief Cooper is back in work in the East Midlands at newly-promoted Premier League side Leicester and has penned a three-year deal.
Baggies head coach Corberan had attracted the interest of the Foxes and, along with Cooper and Graham Potter, was one of three most tipped for the role over the last four or five weeks.
Albion were not prepared to welcome any official approaches for Corberan, but the Spaniard has a release clause in his contract at The Hawthorns, that if met would have led to talks. Burnley have also been linked.
Corberan, his staff and players are due to return to begin pre-season testing next Thursday.