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Squire (24) will join the Highlanders after a couple of years with the Chiefs, while Whitelock (24) heads south from the Crusaders, following four seasons with the Christchurch-based franchise.
The Highlanders now have 29 players on their books - 27 of them returning from last season - and need three more to complete their squad.
The new loose forward duo will fill the sports made vacant by the departure of Nasi Manu and John Hardie.
Squire had a break-out year with the Chiefs in 2013 but was hampered by injury, more specifically concussion issues, last season and made limited appearances for the team.
Squire has been a stand-out for Tasman in the past few seasons, and his ball-carrying ability and all round game will be welcomed by the Highlanders.
Whitelock, an All Black in 2013, has played 50 games for the Crusaders and can play all three loose forward positions.
He has captained Canterbury this season but with Kieran Read at the Crusaders, Whitelock has seen limited minutes at No8.
The two players are a good boost for the Highlanders.
Squire is an abrasive player who makes metres with the ball in hand, while Whitelock works hard all game and makes few mistakes.
The duo will join Elliot Dixon, Dan Pryor, James Lentjes, Shane Christie and Gareth Evans in the loose forwards for the Highlanders next season. The pair have signed one-year deals.
Highlanders coach Jamie Joseph was looking forward to getting Whitelock and Squire into the squad.
''We were looking for a strong ball-carrying eight who would suit our style of play and we believe Liam fits that description. Luke's Super Rugby experience and versatility will be a real asset to our group. We're looking forward to having him join the Highlanders,'' Joseph said.
The Highlanders hope to announce their final three players for the 2016 squad next week.
Canterbury midfielder Rob Thompson is believed to be in the picture, along with Otago back Matt Faddes, while any number of props could make the cut.
The side has only four props on its books at the moment and will want to add another one.
The likes of Ma'afu Fia, Kane Hames and Pingi Tala'apitaga may not return next season.
Six wider training squad players will be named at the end of the month to train with the squad right throughout the season.
Ben Smith, Patrick Osborne, Waisake Naholo, Ryan Tongia, Malakai Fekitoa, Richard Buckman, Jason Emery, Lima Sopoaga, Marty Banks, Hayden Parker, Aaron Smith, Josh Renton, Gareth Evans, Shane Christie, James Lentjes, Dan Pryor, Elliot Dixon, Liam Squire, Luke Whitelock, Alex Ainley, Mark Reddish, Tom Franklin, Joe Wheeler, Josh Hohneck, Ross Geldenhuys, Daniel Lienert-Brown, Brendon Edmonds, Liam Coltman, Ash Dixon.