The defender has fallen out of favour at Parkhead and a proposed loan move to Blackburn Rovers collapsed.
He is now expected to undergo a medical at Hibs this evening ahead of signing a deal until the end of the season.
Hibs are short of options in the centre of defence, with Paul Hanlon and Jordon Forster sidelined by injury and Liam Fontaine picking up a knock against Dunfermline at the weekend.
In addition, Darren McGregor is suspended for Saturday’s Scottish Cup quarter-final against Ayr United.
Ambrose, a Nigerian international who has played in the World Cup finals, has not featured for Celtic since the Champions League qualifying tie against Astana in Kazakhstan in July.