Lugt, who joined the A League club in September 2009 after running the Dutch second division for several years, will stay on until the end of the ACL campaign in May, according to a statement on the team's website.
"I have thoroughly enjoyed continuing building the foundations of our club, in particular by further strengthening the relationship with our fans as well as with the wider community including grassroots football," Lugt was quoted as saying. "Without fans there is no football club.
"I am happy that I have been able to make a contribution to this process during the last 18 months but it is now time to move on."
Local media reports said Lugt had become increasingly frustrated after being sidelined by vice-chairman Scott Barlow, the son-in-law of Russian owner David Traktovenko.
"On behalf of the board I would like to thank Edwin for the contribution he has made to Sydney FC during his time at our club and wish him all the best for the future," Barlow said.
The club, once considered the glamour team of the A league, suffered a terrible season as champions, finishing ninth out of 11 teams this term, and playing in front of dwindling crowds of under 10,000 at their 45,500-seater ground.
Sydney face South Korea's Suwon Bluewings in their opening ACL Group H match at Sydney Football Stadium on March 2.
