Gould steps up from his role as head of football development to take on a new job which encompasses work previously done by Malky Mackay before the former Watford and Cardiff boss stepped down in November.
The SFA has been looking for ways to save money amid the financial challenges posed by the pandemic and the absence of gate receipts from Scotland games.
Gould, who has been with the governing body since 2005, will continue overseeing grassroots football and coach education, and will take on responsibility for elite player development, national team operations and girls' and women's football.
Chief executive Ian Maxwell said: "Andy brings with him a wealth of experience to the role in both grassroots and elite level football and was the outstanding choice to spearhead the development of these key areas.
"In reviewing our operation we identified that we wanted to create greater synergy between our football development and performance areas, with so much of their work overlapping."
Gould has previously assisted with the Scotland youth teams across a number of age levels, including the under-21s, and led the SFA's UEFA Pro Licence coaching cohort.
"Having worked in the development of Scottish football for more than 25 years across all levels, I'm fully conscious of the responsibility that comes with this role in order to capitalise on the opportunities that await Scottish football," he said.
"There are some particularly exciting areas that I look forward to progressing, including the continued growth of the girls' and women's game, the opportunity to harness and build on the inspiration of our men's national team through their participation at Euro 2020 this summer and the opportunity to provide even greater support to our network of clubs across the country.”
"There are fantastic staff working across the development of the game at association level and in our clubs and my intention is to build on those relationships further.
"The immediate priority will be to continue to support our game through this pandemic and put our energies into ensuring people can return to the pitch safely by working with and helping our clubs and coaches at all levels to achieve this.”