The 19-year-old signed for the Premier League champions from A-League sister club Melbourne City last week and will now attempt to realise his impressive potential with a stint in the Scottish Premiership.
A fleet-footed winger, Arzani attracted interest from several European clubs after appearing in each of his country's three matches at the World Cup.
He enjoyed a rapid rise into the national team setup with a series of sparkling performances across 18 appearances in the A-League last season.
The Iran-born attacker will link up with compatriot Tom Rogic at the Glasgow club.
"The idea was put to me to come to Celtic and work with Brendan Rodgers, and it was something I was very interested in doing, and when it became a reality I was very excited," Arzani told his new club's website.
"I gave Tom a call and had a chat with him about the club and everything was positive.
"Basically he said to me that if it wasn't so good he wouldn't have signed an extension to stay at Celtic Park. Apparently, playing in front of the Celtic fans is absolutely amazing and I'm really excited about that."
Arzani's arrival comes just a day after fellow City wide man Patrick Roberts, who had spent the past two and a half seasons with Celtic, sealed a loan move to LaLiga side Girona.