Miles has been at The Hawthorns since 2003, initially as facilities manager, and has held various roles over two decades.
The former Alexander Stadium boss was appointed director of operations in 2016 and has held a place on the board of directors since 2018. He became (non-football) managing director last year.
Gourlay tendered his resignation at The Hawthorns earlier this year and is working his notice period until next Wednesday, June 14.
Miles will retain his title as managing director, meanwhile, and within the Baggies reshuffle head of recruitment Ian Pearce has been promoted to head of football operations.
The managing director will head the club's technical board, featuring Pearce, Carlos Corberan and Tony Strudwick and oversee all club departments.
Pearce was linked with Albion's Championship rivals Stoke City this week but the Express & Star revealed he would remain at the club.
The former recruitment chief has a strong relationship with head coach Corberan and pair have been working closely to put plans in place for the transfer window.
Miles has revealed in a club statement that player sales are inevitable this summer to balance the books by improve increasing income and reducing the wage budget due to the loss of parachute payments and no investment from controlling shareholder Guochuan Lai. He says for the club to maintain stability they must be prudent this summer.
Miles, 47, said: “I am proud and honoured to have been appointed to lead the football club.
“Having spent two decades of my life at The Hawthorns I can assure supporters and staff that I have only ever worked with integrity and in the club’s best interests. This is something I will continue to do.
“There is no escaping the fact the club faces challenges, it’s important I’m clear about that, but I am determined to lead Albion through to a more prosperous period."
The MD adds, though, that Albion plan to build a squad "equipped for promotion" and that sales will help make space to bring in targets with "young, hungry and athletic" attributes. His comments confirm Corberan believes those type of additions can bring success in the Championship.
Miles' comments explain the club see last season's Championship, where Luton won promotion to the Premier League via the play-offs over Coventry, as an example that success can be achieved by working smartly with a lesser budget.
He added: “While some player sales are inevitable, I also recognise the opportunity this provides us to recruit talented young, hungry, and athletic players. The type of players Carlos and the rest of the football technical board believe are required to achieve success in the Championship.
“We have discussed at length the need to refresh the squad this summer and player sales will help us to achieve that while we also work to balance the books.
“Make no mistake, we will be building a squad equipped to compete for promotion – but sales are necessary in order to increase income and reduce the first-team wage bill."
Miles said of new head of football ops Pearce: “In Ian Pearce we have an experienced and knowledgeable football mind who knows what is required to achieve success.
"His already strong relationship with Carlos will only strengthen as they work together even more closely. They have been working together preparing for this transfer window for some time and are very much on the same page in terms of what the club requires."
While assuming the responsibilities and duties from outgoing Scot Gourlay, Miles vowed to continue to meet with representatives of Albion's supporters, where he adds: “I fully understand why supporters are frustrated and fearful.
“I am optimistic that despite the challenges ahead, we can look forward to a successful season and I am confident our incredible supporters will get right behind Carlos and the team when we meet at The Hawthorns again in August."