The versatile Mallia is part of a back three with goal-kicker Emiliano Boffelli and Mateo Carreras on the wings and a powerful midfield of Santiago Chocobares and Lucio Cinti.
Santiago Carreras is at fly-half and Gonzalo Bertranou gets the nod at number nine in what has been Cheika's preferred half-back pairing this season.
Cheika has opted for an extra forward on the bench to keep up the physical pressure on England, and Mallia's ability to cover 10 and 15 gives him that option as it means he can leave Nicolas Sanchez out of the match-day 23.
"We have a lot of confidence in him (Mallia) and in his role," Cheika told reporters on Thursday.
"The first game he played for Toulouse was at fly-half. (He will) touch the ball many times more when he plays at fly-half, a position that requires more responsibility."
The team is captained by hooker Julian Montoya, who packs down with props Thomas Gallo and Francisco Gomez Kodela.
Montoya was Argentina's leading try-scorer at the 2019 World Cup and six of his 11 career tries have come at global tournaments.
The second row is made up of fit-again Matias Alemanno and Tomas Lavanini, who last played as a pair at the World Cup in 2015.
Former captain Pablo Matera is on the flank along with Marcos Kremer, and Juan Martin Gonzalez is at number eight, as Cheika named a 6-2 split between forwards and backs on his bench.
"Given the game we imagine it will be (an intense physical battle), we will have six forwards and two backs in the reserves," he said.
But Cheika said that would not change his team's mindset.
"We have prepared as we always do," he said.
Replacement hooker Agustin Creevy will play in his fourth World Cup, joining Mario Ledesma, Felipe Contepomi and Martin Scelzo for most by an Argentine.
15-Juan Cruz Mallia, 14-Emiliano Boffelli, 13-Lucio Cinti, 12-Santiago Chocobares, 11-Mateo Carreras, 10-Santiago Carreras, 9-Gonzalo Bertranou, 8-Juan Martin Gonzalez, 7-Marcos Kremer, 6-Pablo Matera, 5-Tomas Lavanini, 4-Matias Alemanno, 3-Francisco Gomez Kodela, 2-Julian Montoya (captain), 1-Thomas Gallo
Replacements: 16-Augustin Creevy, 17-Joel Sclavi, 18-Eduardo Bello, 19-Guido Petti, 20-Pedro Rubiolo, 21-Rodrigo Bruni, 22-Lautaro Bazan Velez, 23-Matias Moroni