Colin Fleming, the Billie Jean King Cup coach and former Davis Cup player, will take step into the role on in interim basis after Azevedo agreed to end his contract following a period of compassionate leave.
Fleming has worked closely with the academy players since the academy was set up two years ago and will step up while Tennis Scotland and the LTA agree the recruitment process for Azevedo's successor.
Blane Dodds, Tennis Scotland Chief Executive, said: “All of us at Tennis Scotland, and of course the players and coaching staff at the National Tennis Academy, are really sad to see Leo leave his role as Head Coach.
"We fully support his decision to remain at home to support his family during a challenging time and appreciate the commitment he has made to the next generation of players at the GB National Tennis Academy during his two years at Stirling.
“I would like to wish Leo all the best for the future and we will ensure that a relationship is maintained between both parties.”
Azevedo stated: “It has been a privilege to serve as the Head Coach of the GB National Tennis Academy and it is a role I will proudly reflect on throughout my career. I’m devastated to cut short my time here in Scotland as I’ve had such a positive experience.
"I send my best wishes for the continued evolution of the academy and look forward to keeping track of the development in coming years.”