The Barclays Premier League side had two offers for the 26-year-old turned down ahead of the Parkhead club's midweek loss to Legia Warsaw at Murrayfield. However, as one Celtic source told Herald Sport, they never really stepped away from the negotiating table and finally put forward a package appealing enough to secure an agreement during the course of last night.
Forster is pencilled in to undergo a medical and discuss personal terms over the weekend with a four-year contract understood to have been sanctioned by Ronald Koeman, the Southampton manager.
Newcastle United are due to receive a cut of the fee under the terms of the deal that saw Forster move to Glasgow for £2m in 2012 in the wake of a successful loan spell, but the Celtic chief executive, Peter Lawwell, will now be under pressure to use these funds to strengthen the squad.
Manager Ronny Deila has already stated that he expects to receive a percentage of any fees brought in to reinvest in new talent and the need for new recruits has been made all the clearer following the incredible reprieve that has set up a Champions League qualifying play-off with NK Maribor of Slovenia.
Celtic, of course, lost 6-1 on aggregate to Legia Warsaw in the second qualifying round, but the Polish club have been punished by UEFA for fielding a player that was technically suspended and have to give up their place to the team they conquered pending an appeal.
Deila faced the media yesterday afternoon and was suitably calm about the prospect of losing some of his leading players with Virgil van Dijk, Adam Matthews and Kris Commons also attracting interest from England.
"Everything can happen," said Deila. "I have lived through these transfer windows and you must adjust. Someone goes out and someone comes in. That kind of circulation can be good for the team.
"When you are a winning team, it's very important to get new faces in. You keep up the energy and the challenges within the side.
"Still having the Champions League could also make it easier to get players in."
Forster set a new Scottish league record for consecutive clean sheets, passing former Aberdeen goalkeeper Bobby Clark's achievement from 1971, by going 13 matches and 1,256 minutes without losing a goal.
He earned a place in the England squad for the World Cup on account of his form at Celtic - although he did not play as Roy Hodgson's third choice - and leaves with Craig Gordon, brought in on a free transfer over the course of the summer, and Lukasz Zaluska now vying to be Forster's permanent replacement.
Gordon conceded six goals in a friendly with Tottenham Hotspur in Helsinki last weekend, but insists he is fit enough play regularly after more than two years struggling with knee problems.
"The knee is holding up," he said. "I can kick the ball, chuck the ball about and kick it long into the other team's half. Those are the things I had struggled to do."