Arzani featured in all three of Australia's games at the World Cup after making 18 appearances and scoring two goals in the A-League for Melbourne in 2017-18, and he was named the league's Young Footballer of the Year.
He was the youngest player ever to be named in Australia's squad for a World Cup and was also the youngest player at the tournament in Russia, making his first appearance in the second half of the Socceroos' 2-1 defeat to France.
Arzani is expected to be sent out on loan, with Scottish champions Celtic his destination.
City's managing director of global football, Brian Marwood, told the club's official website: "In a short period of time, Daniel has developed into one of Australia's brightest young stars and has demonstrated the drive and raw talent required for success at the highest level.
"This pathway was first forged by Aaron Mooy just two years ago, and we are all delighted to see another Australian-grown talent make this move.
"The combination of City Football Group's global football structure and the world-leading City Football Academy facilities create an environment in which this pathway can become well-trodden."
Arzani, who was in the stands for the Glasgow's side's 1-1 draw against AEK Athens in Champions League qualifying on Wednesday, is set to join Celtic on a two-year loan deal, and the young attacker's national team boss, Graham Arnold, has backed the player to hit the ground running.
"It's a big move for the kid," Arnold told reporters. "He's a very intelligent kid. He knows what his plans are.
"The most important thing, and he's aware of that, is wherever he goes he has to play.
"He believes in himself a lot. He believes going to Celtic he will get to play more games in Scotland and being part of a Champions League squad than he probably would here in Australia.
"I'm sure he will do exceptionally well."