Players who miss those two squads will be eligible for an Argentina XV.
While included in the squad missing from the Argentina lineups until just before the World Cup, will be flanker Marcos Kremer. He is under a five-week suspension from the French Top 14 game between his club Stade Francais and Racing 92. Kremer was given a red card after direct shoulder-to-head contact with Racing's first five-eighths Finn Russell.
Kremer will miss Argentina's Rugby Championship games against the All Blacks, Australia and South Africa and another warm-up game against the Springboks.
Cheika has drawn his players from Australia, Italy, England, France, Ireland, Japan, New Zealand, Scotland and Wales while including two players from Argentina's Sevens side.
While the squad's primary focus is the Rugby Championship, the Argentina XV will play four Rugby World Cup warm-up games against Uruguay and Namibia and two games against Chile.
New to the international squad are Sevens players Luciano Gonzalez and Rodrigo Isgro. Also included is wing Martin Bogado, who played for the Highlanders during Super Rugby Pacific this year.
The squad (with their clubs in brackets) is:
Loosehead props: Iganacio Calles (Pau), Thomas Gallo (Benneton), Nahuel Tetaz (Benetton), Marco Vivas (Gloucester).
Hookers: Facundo Bosch (Bayonne), Agustin Creevy (London Irish), Julian Montoya (Leicester), Santiago Socino (Gloucester), Ignacio Ruiz (London Irish).
Tighthead props: Eduardo Bello (Newcastle), Francisco Gomez Kodela (Lyon), Santiago Medrano (Force), Joel Sclavi (La Rochelle), Lucio Sordoni (Glasgow).
Locks: Matias Alemanno (Gloucester), Tomas Lavanini (Clermont), Guido Petti (Bordeaux), Lucas Paulos (Bayonne).
Flankers: Juan Martin Gonzalez (London Irish), Santiago Grondana (Pau), Facundo Isa (Toulon), Marcos Kremer (Clermont), Pedro Rubiolo (Newcastle).
No8: Rodrigo Bruni (Bayonne), Pablo Matera (Honda), Joaquin Oviedo (Perpignan).
Halfbacks: Lautaro Bazan Velez (Rovigo), Gonzalo Bertranou (Dragons), Tomas Cubelli (Biarritz), Gonzalo Garcia (Zebre).
First five-eighths: Tomas Albornoz (Benetton), Santiago Carreras (Gloucester), Nicolas Sanchez (Brive).
Second five-eighths: Santiago Chocobares (Toulouse), Jeronimo de la Fuente (Perpignan), Matias Orlando (Newcastle).
Centres: Lucio Cinti (London Irish), Luciano Gonzalez (Pumas Sevens), Matias Moroni (Newcastle).
Wings: Emiliano Boffelli (Edinburgh), Sebastian Cancelliere (Glasgow), Mateo Carreras (Newcastle), Santiago Cordero (Connacht), Bautista Delguy (Clermont), Juan Imhoff (Racing 92), Rodrigo Isgro (Pumas Sevens).
Fullbacks: Martin Bogado (Highlanders), Juan Cruz Mallia (Toulouse).