The 49-year-old reportedly had a deal to remain in charge next season, despite it having previously been claimed that he needed to secure a spot in the top four to earn an extension.
But his failure to do so, followed by last Friday's 2-1 elimination final defeat away to Melbourne Victory, has sealed the fate of the former Australia boss.
The club issued a statement on Wednesday confirming they had moved to dismiss Farina.
"Frank joined us as coach in a difficult period last season and has always given his absolute dedication and commitment to the club," chairman Scott Barlow said.
"Frank has shown great integrity and resolve in what has been often challenging circumstances this year.
"I would like to pay tribute to Frank for his professionalism and wish him well for the future."
Farina took over from Ian Crook in November 2012, but could only take Sydney to seventh in the table in 2012-13.
Former Central Coast Mariners boss Graham Arnold, who is reportedly in talks with the Newcastle Jets, is also likely to be on Sydney's radar.
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