Celeski is expected to arrive in the Middle East on Tuesday night for a medical before putting pen to paper on a reported one-year deal worth around $500,000.
The 28-year-old, whose Victory contract was due to expire at the end of the season, was the only player to face both Manchester United and Liverpool as part of their recent tours of Australia.
Celeski, who joined Victory from Perth Glory in 2008, has established himself as one of the A-League's most consistent midfielders with 123 appearances in Australia's top tier.
"Billy has been an integral part of Victory’s team over 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," Victory coach Ange 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."
Al Shaab, who last week missed out on the signature of Sydney FC midfielder Nick Carle, are looking for improvement after finishing 12th in the UAE's top tier of football last season.
With the new campaign of the re-badged Arabian Gulf League Pro League set to begin on September 14, Al Shaab identified Celeski as key to their hopes.
Celeski's departure is another blow to Victory's stocks after the club failed in their attempts to sign Greece captain Georgios Karagounis and Italian midfielder Fabrizio Miccoli earlier this month, while Mark Milligan remains linked with a move to English Premier League outfit Crystal Palace.
