The former Real Betis boss was originally rejected by the Baggies over backroom staff disagreements but has now penned an 18-month deal and will be supported by Keith Downing
Clarke was sacked on December 14 following a run of four straight Premier League defeats, leaving the Baggies just two points away from the relegation zone before caretaker Keith Downing oversaw three draws and a win.
Mel, who has penned an 18-month contract, was sacked by Real Betis in December after a poor start to the season but guided the club to a seventh-placed finish, and the Europa League, last term.
"His appointment concludes an extensive recruitment process during which we have cast the net far and wide to identify the most suitable candidate to take the Club forward," director Richard Garlick told the club's official website.
"Pepe was a strong contender from the outset due to his impressive achievements and has emerged as our No.1 candidate.
"He is a forward thinking coach whose teams are renowned for playing an attractive and positive style of football."
Mel originally held talks with West Brom in December but negotiations collapsed after the Spaniard made it clear he intended to bring in his own backroom staff.
Downing will now support Mel, with Saturday's trip to Southampton the caretaker's final game in charge.