Al Shaab, which last week failed in a bid to snare Sydney FC’s Nicky Carle, finished 12th in the 14-team UAE Pro-League in 2012-2013 and is looking to Celeski to help spark a revival when its season kicks off against Al Jazira on 14 September.
It's been a big few weeks for Melbourne-born Celeski, who was the only player to take on both Manchester United and Liverpool FC, as part of their recent tours of Australia.
Celeski was one of the most consistent midfielders in the A-League in season 2012-2013, completing more passes than any other player.
Melbourne Victory coach Ange Postecoglou said Celeski had made a significant contribution to the club since he joined in 2008.
"Billy has been an integral part of Victory's team for several years and in the past week or so we have seen him perform very well against some of the best midfielders in the world," Postecoglou said.
"We wish Billy all the best for the upcoming season in the Middle East and I'm sure many of our fans will be keeping a close eye on his performances, albeit from afar."
Celeski scored six goals in his 123 A-League appearances, won the Premiership/Championship double in his first season with Victory in 2009 and made one appearance for the Socceroos, also in 2009.