Here, we look at five of the potential candidates to replace the Scot.
Roberto Di Matteo
Di Matteo, installed early on as the bookies' favourite to succeed Clarke, would be returning to a club he guided into the top flight in 2010 before being relieved of his duties in February 2011. The former Italy international has since had a spell in charge at Chelsea from March to November 2012, during which the Blues won the Champions League and the FA Cup. Given that success, he would appear to be a decent option, although Albion chairman Jeremy Peace may well be reluctant to appoint someone he fired from the same job not so long ago.
Jol also has West Brom connections, with the Dutchman having been a Baggies player in the 1980s. The ex-Tottenham manager can point to plenty of Premier League experience on his CV, but the fact he was recently sacked by Fulham is hardly a recommendation of his credentials.
McInnes is another former West Brom player and the Scot has been linked with the job of Albion boss before. But he is currently at Aberdeen, who he only took charge of earlier this year, and could be regarded as a risky choice given he is yet to have managed in the English top-flight.
Ole Gunnar Solksjaer
The ex-Manchester United striker has won trophies in his native Norway with Molde since being named their boss in 2011 and often gets mentioned when English vacancies come around. But a lack of experience of managing in a top-level European league - and in Solskjaer's case, simply of being a number one - might be something Albion look to avoid with this appointment, particularly given Clarke was in his first managerial position at the Hawthorns.
The German has not managed in the Premier League but he has plenty of Bundesliga experience and reportedly held talks with Albion about taking charge at The Hawthorns prior to Clarke's arrival. Has been working as a sporting director at Leipzig and Salzburg.