Milicic was a founding member of the Heart's coaching panel, spending two years working with inaugural senior mentor John van 't Schip.
When van 't Schip left at the end of the 2011-12 season, the Heart chose John Aloisi as his successor, rather than the more experienced Milicic.
Heart CEO Scott Munn said Milicic had made an immense contribution to the club.
"Ante had a substantial role in the establishment of our playing roster and implementation of the playing style and philosophy which is now our trademark," Munn said.
"While obviously disappointed to see Ante leave, we understand the significance of the opportunity which presented itself in helping establish a team in his home town."
Popovic - a close friend of Milicic - quit English club Crystal Palace last week to join the as-yet unnamed western Sydney outfit.