Salvachua stepped up from his role as assistant coach in January after Marco Kurz's sacking through just 13 matches in charge.
Victory was second from bottom in the A-League after 21 matches when the season was suspended because of the coronavirus pandemic, while Salvachua had secured the club's place in the AFC Champions League group phase.
But the 47-year-old Spaniard will not return to Melbourne as the A-League prepares to restart in July, opting to continue his coaching career in Europe and to be closer to his extended family in Spain.
"On behalf of everyone at Melbourne Victory we would like to thank Carlos for his professionalism, hard work and commitment to our club over the past two seasons," Victory chief executive Trent Jacobs said through a statement on Saturday, with the club already in the process of searching for a new permanent coach.
"Given the current environment around the world and the fact we are working through a process to appoint our next A-League head coach, we understand and accept Carlos' decision to return to Europe.
"Carlos arrived as Kevin Muscat's assistant ahead of the 2018-2019 season, before stepping up as head coach during the 2019/20 season. Carlos' short tenure as head coach included securing our club's first away win in the AFC Champions League, ultimately seeing us qualifying for the 2020 group stage. We wish Carlos and his family a safe return to Europe and we wish him all the best for the next chapter in his coaching career."
Salvachua, who joined Victory as an assistant in 2018-2019, added: "I would like to thank Melbourne Victory for the way they have looked after myself and my family since we arrived in Australia.
"It has been a pleasure to help coach the club over the past two seasons. The decision to return to Europe is an opportunity to continue my coaching career, and the other major upside which is to be closer to our extended family in Spain.
"I want to personally thank the Victory board, players, football and administration staff for all their hard work and support and thank you to the members and fans for supporting the team. I wish everyone at Victory all the best for future. Continue to look after each other and stand by the club. Adios and thank you Melbourne."