Hughton, who left Norwich in April as his side slumped towards relegation, is joined by former Cardiff boss Malky Mackay at the top of the bookmakers' shortlists.
The end of Mel's five-month stay at The Hawthorns looked inevitable despite doing enough to maintain their place in the Barclays Premier League.
West Brom sporting and technical director Richard 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, 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."
Mel had cut a resigned figure after his side's final day defeat to Stoke on Sunday and his no-nonsense statements in the post-match press conference suggested a man who knew his time was up.
He was known to have been unhappy with the way the club dealt with a number of off-field issues during the season and his claim the club needed "eight or nine" new players over the summer will not have gone down well.
Mel had added: "West Brom still have time to decide whether or not they want next season to be one as full of as many problems as this one."
Assistant head coach Keith Downing and goalkeeper coach Dean Kiely will remain in their current roles with the club although first-team coach David Gomez has left his post.
Other names being suggested include former Baggies midfielder and current Aberdeen boss Derek McInnes, Celtic boss Neil Lennon and current Tottenham boss Tim Sherwood.
- Sports & Recreation
- Barclays Premier League
- Malky Mackay