The German, 50, replaces Kevin Muscat at the A-League giants, remaining in Australia after leaving Adelaide United.
Kurz, who has also previously coached the likes of 1860 Munich, Kaiserslautern and Hoffenheim, won the 2018 FFA Cup with Adelaide.
"It's an honour to be named as head coach of Melbourne Victory, a big club with a strong history, passionate fanbase and true drive for success," Kurz said in a statement on Friday.
"I've got to know Melbourne Victory from afar, and had tremendous respect for them during that time, so it is exciting to join the club.
"During the interview process we had aligned beliefs about the direction forward which was very important. I can't wait to join the team and get underway."
Victory chairman Anthony Di Pietro was delighted to welcome Kurz, who will arrive at the club within a fortnight.
"Our panel of experienced football people including Mark Bresciano, Paul Trimboli and Rob Sherman, undertook a comprehensive recruitment process," he said.
"Coupled with his international and domestic experience, Marco demonstrated outstanding qualities throughout. Importantly his passion for success and desire to win is aligned with our club's ambition.
"We look forward to working together to bring excitement and success for the Victory family and are confident Marco will do an outstanding job in the high-pressure role."
Victory has seen the likes of Keisuke Honda, Raul Baena, Kosta Barbarouses and Georg Niedermeier leave since the end of the season.