The 13-year-old became the youngest player to turn out for the New Douglas Park Under-20s in midweek when he played the final six minutes of Accies' 3-1 win over Partick Thistle.
Rae has had a trial at Everton and was due to go back to Merseyside for a second stint with Brendan Rodgers' side but he has now chosen to sign for his boyhood heroes, and made the switch to Parkhead after two seasons in Lanarkshire.
Hamilton Academy director Allan Maitland said: "His family have decided his future lies with Celtic.
"I am disappointed to lose another player, but I recognise that, as a Celtic supporter, when Celtic come calling, it is hard to resist. My argument was that he has developed better with us since leaving Celtic two years ago, but he will be signing for Celtic next week after he attends a Scotland trial."
Croy-born Rae has attracted widespread interest and travelled to Spain last year for a trial with La Liga giants Atletico Madrid after impressing for Hamilton's youth sides.
Accies turned down two offers for his services before the kid keeper finally clinched his dream move and Maitland is confident the cash received will be put to good use as the Lanarkshire side look to produce more stars of the future.
He said: "Celtic have been very professional, have handled it in the right manner and the compensation will be slightly more than what would have been due had he left at the end of the season."