The 50-year-old Spaniard has signed an 18-month contract and takes over the reins from Keith Downing, who took charge of the team in a caretaker capacity five games ago.
Mel arrives at The Hawthorns with 14 years' coaching experience in Spanish football, having steered previous club Real Betis to a seventh-place finish in La Liga last term and qualification for the Europa League.
Madrid-born Mel will be supported by Downing and Dean Kiely, who will continue in their present roles as Assistant Head Coach and Goalkeeping Coach respectively.
Sporting & Technical Director, Richard Garlick, said: "I'm delighted to welcome Pepe to the Club.
"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.
"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."
Downing, who has conducted this week's pre-match preparations, remained in charge for Saturday's trip to Southampton while Mel observed his new team from the stands.
Mel's first game at the helm will be the televised home match against Everton on Monday week.
Garlick added: "The Board is extremely grateful to Keith, the coaching staff and players for their efforts over the past month, which has yielded six points from four unbeaten league games.
"Keith will have an important role to play in supporting Pepe as he coaches in England for the first time."