Robson, who resigned from the same position at Essendon in the wake of the AFL club's doping scandal, will leave the A-League heavyweights before Christmas to join Rowing Australia.
Board member Richard Wilson will act as managing director as Victory begins a search for a new boss.
Robson, who began his stint at at Victory in July 2013, will remain at the club until December 22.
Chairman Anthony Di Pietro thanks Robson for his contribution to the club in his four and a half-year tenure.
Robson admitted he was sad to leave the a-League club.
“I’ve thoroughly enjoyed my time at Melbourne Victory and while it’s with some sadness that I move on, the time is right for me to explore another opportunity," he said.
“I’ve derived enormous satisfaction from what the club has been able to achieve over the past four and a half seasons, both on and off the field.
"I’ve no doubt the club will continue to go from strength to strength.