Mel will be supported by Downing and his number two Dean Kiely who will remain with the club as assistant head coach and goalkeeping coach respectively.
Downing took charge after Scot Steve Clarke was sacked on December 14 following a sequence of one victory in 10 league games.
"I'm delighted to welcome Pepe to the club," said Albion's sporting and technical director Richard Garlick.
"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 emerged as our number one candidate," said Garlick.
"He is a forward thinking coach whose teams are renowned for playing an attractive and positive style of football."
Mel arrives at West Brom with 14 years of coaching experience in Spanish football.
He led Betis into this season's Europa League but was sacked at the start of last month with the club bottom of La Liga.
Albion said Downing would remain in charge for Saturday's league game at Southampton while Mel observes his new team from the stands.
The new manager's first game at the helm will be the home match with Everton on January 20.
"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," said Garlick.
"Keith will have an important role to play in supporting Pepe as he coaches in England for the first time."
West Brom are 14th in the table, four points above the relegation zone.
(Writing by Tony Jimenez, editing by Pritha Sarkar)
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