The snaring of the attacking midfielder is the first blow in what promises to be a hard fought battle to sign players with the new and unnamed western Sydney side coached by Tony Popovic.
Abbas, 25, was a member of Iraq's 2007 Asian Cup winning team and has spent the past three years with the Newcastle Jets.
Abbas agreed to terms over the weekend and trained with the Sky Blues on Monday.
Crook is delighted to have signed the gifted speedster who is sure to add plenty of punch to Sydney's attacking stocks.
"I believe Ali is a fantastic addition to the squad and will have a big impact on the team," he said.
"He has great endurance and is very quick. 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 beaten off competition from other clubs for his signature and he will prove to be a very exciting signing for the Sydney FC fans."
Abbas was thrilled to link with Sydney's exciting line-up that includes young guns Joel Chianese, Terry Antonis and Mitchell Mallia.
"Sydney FC has a strong squad and a great coaching staff, and I look forward to working with both ... now I'm ready to focus on training for next season, and help the team challenge for another title," he said.
Abbas fled war-torn Iraq after playing an under 23s international against the Olyroos in Gosford four years ago and was granted asylum to stay in Australia.