Tom Rogic and Nir Bitton will end nine-year spells with Celtic this summer, with manager Ange Postecoglou saying it was a joint decision with the players.
The midfielders have won 34 domestic honours between them at the club.
They will leave after Celtic are presented with the Scottish Premiership trophy against Motherwell on Saturday.
"Both of them felt like it was the right time and we as a club agreed," Postecoglou said. "It was never about one party or the other."
The pair, signed during Neil Lennon's first spell as manager, exit despite the Australian describing their role as "crucial" in helping his side win the title and League Cup this season.
Postecoglou said 29-year-old Australia international Rogic, who has scored 44 goals in 272 Celtic appearances since arriving from Central Coast Mariners, was "outstanding", "unbelievable" and "probably as fit and as strong as he's been physically during his whole career at Celtic".
The 30-year-old Bitton, who has played 270 times since moving from Ashdod, was a less regular starter this season but had an "important" role both on and off the park, proving an "immense" influence in helping fellow Israel international Liel Abada make an impact as a 19-year-old at his first club away from home.
Postecoglou explained that their impending departure had been decided following discussions earlier in the season and the fact that both players had spent so long on "the other side of the world" played a part.
"Fortunately, we get to honour two of our greats and say goodbye in front of 60,000 at Celtic Park as champions," he said.
Postecoglou pointed out that an early decision on their future allowed him to sign midfielders Matt O'Riley, Reo Hatate and Yosuke Ideguchi in January and means "we don't have to bring too many in that area in the summer window".
The manager expressed his delight that "one of the greats" James Forrest had "stuck around" by signing a three-year contract extension despite "a frustrating couple of years" for the 30-year-old Scotland winger.
"Part of building a team and building a culture is that you need constants through that - people who have won things, who understand this football club," he said. "I still think he's got a lot to offer us."
Meanwhile, Postecoglou confirmed that Celtic would take up the option to turn the loan that also brought striker Daizen Maeda from Yokohama F. Marinos in January into a permanent transfer.
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