The former Real Betis coach was in the stands to watch the 1-0 loss to Southampton on Saturday, two days after being officially appointed on an 18-month contract.
Caretaker boss Keith Downing took charge for the final time at St Mary's Stadium, his five league games at the helm yielding a win and three draws before his unbeaten record came to an end with the reverse at Southampton.
Mel takes over a side who have won only once in their past 12 matches in all competitions, a run that has left them looking over their shoulders towards the relegation zone just three points below.
West Brom have won four of the last six meetings between the sides at the Hawthorns, keeping a clean sheet in each of those victories, although on Monday they will have a familiar face to contend with in Romelu Lukaku.
The Belgium international striker spent last season on loan at the club from Chelsea, scoring 17 goals.
Everton are enjoying a fine first season under the stewardship of Roberto Martinez, their two defeats from 21 league matches the lowest total in the division, while no team in the league has drawn more games than either of these two sides, West Brom recording nine and Everton eight.
The 1-0 home defeat to Sunderland on Boxing Day was Everton's only loss in the last 14 Premier League games, and they have won three and drawn the other of their four matches in all competitions since.
Both sides saw strikers depart for Hull City in the week, Nikica Jelavic leaving Goodison Park, while West Brom's Shane Long also signed for Steve Bruce's side.
Aiden McGeady, signed from Spartak Moscow last week for an undisclosed fee, could be in line to make his Everton debut, with Sylvain Distin set to return from a hamstring problem, while Ross Barkley is likely to miss out with a fractured toe.
