Spaniard Mel has replaced Steve Clarke at The Hawthorns on an 18-month contract, although Downing will remain in charge for Saturday's Premier League visit to Southampton.
Downing, along with goalkeeping coach Dean Kiely, will remain at the club to assist former Real Betis boss Mel.
"It's exciting times," said Downing. "It's one that has done a full circle and I am pleased personally that it has settled down and we have now got somebody in place.
"An 18-month contract brings a bit of stability to the football club. I think that's what was what needed so I am pleased from that point of view because to be honest it has been a little bit unsettling - particularly this last week.
"We have had a lot of rumours flying around, the players have been trying to get on with things and they have done very well.
"I wasn't sure if I was going to focus in on the Southampton game as I wasn't sure it if it was going to be done earlier. But as the week has progressed I have got more focused on the game and we will concentrate on that on Saturday."
Downing has yet to meet Mel but the pair are set to speak this weekend with the Spaniard due at St Mary's to watch the game from the stands.
"I am aware that he is going to watch the game on Saturday and then we crack on next week," said Downing.
"I have heard good things about Real Betis, the fact that he has got them up and stabilised them.
"The Spanish press are quite positive about him but he is a name I wasn't aware of until a few weeks ago.
"He fits the criteria. He wants to play attacking, positive football for the football club. It's a new way forward so it is exciting."
Mel reportedly speaks very little English but Downing does not believe that will be a problem.
He said: "It is going to be an interesting time. We are aware that there is going to be help coming along in terms of the translations but football is a universal language and I am excited to be able to work with someone with maybe some new ideas."
There are reports in Spain that Mel will bring in his own staff during the summer but Downing believes the current coaching structure will remain in place.
He said: "I know there have been rumours flying around but I trust the football club to do what it has done over the last five or six years.
"There has always been a structure in place here. The club has stabilised itself and established itself in the Premier League.
"It has been successful with that formula and I think the outside looking in has respected what the football club does - the fact that there is not too many changes.
"There is always the opportunity for a man to come in to have a second man with him but the structure is good. The staff are good right the way through the football club and it has worked - 12th 11th and eighth in previous seasons - it has been successful."