Sydney head coach Ian Crook swooped on the Iraq international after he was axed by the Jets last week.
Abbas, 25, is the first player to join the Sky Blues since Crook was handed the reins earlier this month.
"He has great endurance and is very quick," Crook said.
"He is also naturally left-footed which is something we've been missing on the left wing recently.
"I think we are very lucky to have won his signature and he will prove to be a very exciting signing for the Sydney FC fans."
Abbas was part of the Iraq side that won the Asian Cup in 2007 and has three years of A-League experience under his belt.
"Sydney FC has a strong squad and a great coaching staff, and I look forward to working with both," Abbas said.
"Now I'm ready to focus on training for next season, and help the team challenge for another title."
Abbas grabbed global headlines in 2007 by seeking asylum in Australia after playing for Iraq in an Olympic Games qualifier in Gosford.
He spent time with the Marconi Stallions in the New South Wales Premier League before joining the Jets, where he made 60 A-League appearances.