The former Tenerife and Real Betis boss was brought in by Albion to replace Steve Clarke after his dismissal last December.
Albion finished fourth from bottom in the Premier League, just three points ahead of relegated Norwich.
The Baggies won just three of their 17 games during Mel's tenure, drawing six and losing eight, which left him with a win percentage of only 18.
Following discussions between the West Brom board and Mel, Albion's sporting and technical director Richard Garlick confirmed the decision.
Garlick said: "We would like to thank Pepe for his efforts over the past four months in helping to keep the club in the Premier League and wish him well for the future.
"Both Pepe and the club set out with the best intentions of making the appointment work. However, having reflected on events both on and off the field during our talks today, it became apparent that it was in the best interests of both parties for there to be an amicable parting.
"We are grateful for the manner in which the existing coaching staff and players have rallied behind Pepe to get the club over the line in what has proved an extremely competitive division."
David Gomez has also left West Brom following the completion of his coaching contract, but assistant head coach Keith Downing and goalkeeper coach Dean Kiely will remain in their current roles.
Garlick added: "Although we have managed to achieve a fifth successive season of Premier League football, it has been a very disappointing campaign and lessons have been learned.
"The search for a new head coach has now begun. We aim to find the most suitable candidate who, with the support of the structure we have had in place for six years and are presently strengthening, will enable the club to be more competitive next season."
Sky Bet have installed Malky Mackay as favourite for the post from Chris Hughton (7/2) and Tottenham's Tim Sherwood (8/1).