The Australian club announced on Friday morning that a fee had been agreed with City for the 23-year-old and a club spokesman has confirmed the completion of the deal.
Caceres is not seen as a player who could challenge for a first-team spot any time soon and he could well be loaned out.
Mariners head coach Tony Walmsley signed Caceres in 2011, and he told the club website: "We need to celebrate when players at the Central Coast Mariners are sold to bigger clubs. It's our charter. It's our intent.
"When I brought Anthony Caceres to the Mariners his potential was obvious.
"This move demonstrates how far Anthony has progressed and symbolises how giving youth a chance works for both the Central Coast Mariners and young aspirational footballers."
An obvious destination for Caceres would be City's A-League sister club Melbourne City.
The league does not allow clubs to buy players from each other but a loan from Manchester City would be allowed.
Melbourne boss John van't Schip was coy on any loan move, with the Dutchman quoted in the Australian press saying: "Manchester City is getting him in. More or less, that's it.
"We can't comment on (a potential loan move) but of course everybody knows he's a good player, he's one of the better players in the A-League. So we'll just have to see."