The 54-year-old, who has experience in South America, Europe and the United States, has taken a two-season contract to replace Arthur Diles.
Savarese has coached in the US, initially at New York Cosmos whom he steered to three NASL championships in 2013, 2015 and 2016.
Savarese then spent five-and-a-half-seasons as coach of MLS club Portland Timbers.
As a player, Savarese earned 30 caps for Venezuela, scoring 10 international goals, in a career also including stints in South America, Â the US, Italy and the United Kingdom.
Victory chairman John Dovaston described Savarese's appointment as a bold new direction designed to enhance the club with international experience.
"We are delighted ... his experience as a player and coach across multiple continents, together with his character and football philosophy, aligns strongly with Melbourne Victory," Dovaston said in a statement on Thursday.
Melbourne Victory managing director Caroline Carnegie said Savarese's international experience was the clincher in winning the job.
"Giovanni's appointment reflects a deliberate decision to bring a fresh perspective to the club," she said in a statement.
"What stood out throughout the recruitment process was not just his attacking football philosophy, but the fact that Giovanni has succeeded in a competition with strong parallels to ours."
Savarese said he was impressed by Victory from the outset when applying for the job.
"From my very first conversations with the club, I felt a strong connection to its vision and its values," he said in a statement.
"I know how much Melbourne Victory means to its supporters.
"And I can assure them that we will work tirelessly and play with real ambition to build a team they can be proud of and to compete for the biggest honours."
Meanwhile, Western Sydney Wanderers have split with a batch of players including Alou Kuol, Josh Brilliante and Kosta Barbarouses.
The trio, along with Bulgarian Bozhidar Kraev, Phillip Cancar, Jacob Farrell and Ruon Tongyik, have been told they won't be offered fresh contracts.
And Central Coast Mariners have also told a decorated trio - Nathan Paull, Miguel Di Pizio and Christian Theoharous - they are no longer required.
The trio were all part of the Mariners' historic treble in 2023-24, with former captain Paull joining rivals Macarthur FC.
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