After two failed bids by the English Premiership outfit, a fee has now been agreed between the clubs.
Forster will undergo a medical in London on Saturday morning, after which the transfer will be concluded.
He joined Celtic on loan from Newcastle in 2010, and a full £2m transfer followed two years later.
The news of Forster's departure came on the day Celtic were drawn against NK Maribor in the play-off round for the Champions League after dramatically winning re-instatement to the competition.
The Hoops will travel to play in Slovenia on August 19/20, with the return leg taking place at Celtic Park a week later. The Hoops have never met the Slovenian champions, who defeated HSK Zrinjski from Bosnia and Maccabi Tel-Aviv to reach the play-offs.
Maribor have only made it to the group stage once, in 1999/2000. They knocked Rangers out of the Europa League at the play-off stage of that tournament three years ago.
That gave the Slovenians revenge for having lost out to the Ibrox club in the Champions League qualifiers in 2001.
Win or lose in the play-off, Celtic are now guaranteed European football through to December, either in the group stage of the Champions League or the Europa League.
They aim to take their second chance in the premier competition after Uefa decreed Legia should forfeit the 2-0 win against them on Wednesday.
A disciplinary hearing held at their HQ in Switzerland found them guilty of fielding an ineligible player in their third round qualifying tie at Murryafield.
The Polish club plan to appeal. Their chairman, Dariusz Mioduski, said: “Today, the sport lost behind closed doors. We made a mistake. Sorry, but the penalty is disproportionate. Stay with us. We fight on.”
For now, however, Celtic are in the Champions League, and Legia the Europa League.
The victory in Edinburgh for the Polish side was forfeited, and Celtic were awarded a 3-0 win.
With the first leg in Warsaw having ended 4-1 for Legia, that made the aggregate 4-4 – and Celtic go through to today’s play-off round draw under the away goal rule.
Legia had fielded Bartosz Bereszynski as a substitute for the final four minutes of the tie in Edinburgh when the defender was still serving a suspension.
Bereszynski was sent off in Legia’s final Europa League game last season, against Apollon Limassol, and was handed a three-game ban.
Legia believed he had served the first two of these games when they eliminated Dublin club, St Pat’s, in the second qualifying round of this season’s competition.
And, having also sat out the first leg tie against Celtic, the Polish champions believed his suspension had been completed.
Celtic were not aware of the rule infringement, and did not make a protest.
However, a Swiss Uefa delegate, Paul Krahenbuhl, noticed Bereszynski had not been included in the squad Legia registered with Uefa for the games against St Pat’s.
And, under the competition rules, that meant these two games did not count towards serving his suspension.
Effectively, the clock did not start ticking on his Bereszynski’s ban until he was included in their squad list, which he was for the ties against Celtic.
Legia’s written representation argued his four-minute involvement when they were five goals ahead on aggregate had no material effect on the result, and that it was down to a misinterpretation of the rules, not an attempt to gain an unfair advantage.
However, Uefa decided they were guilty of breaking their rules by fielding an ineligible player, and the automatic sanction for this is a 3-0 defeat.
Legia were then included in today’s draw for the play-off round of the Europa League.
The Poles have five days to appeal and have asked for Uefa’s reasoning.
It is the second time in three years Celtic have profited from opponents breaking Uefa rules.
In 2011, Sion defeated the Parkhead club in the play-off round for the Europa League, but were subsequently found to have fielded five ineligible players who had been recruited by the Swiss club while they were still operating under a signing embargo for a previous rule infringement.
Sion eventually took their case to the Court for Arbitration in Sport, but this independent body found in Uefa’s favour.
Meanwhile, Arsenal will meet Turkish side Besiktas in the two-legged play-off.
Arsene Wenger’s side, who finished fourth in the Premier League last season, will travel to Istanbul for the first match in the week beginning August 18, with the home leg taking place the following week.
Arsenal have never previously met Besiktas in any Euro competition.