The prop duo are currently training with the Scotstoun side, providing competition for places over the next few weeks.
Capped five times by Argentina, the 34-year-old stands at 5'11" and weighs in at 109kg.
28-year-old McQuillan joins the squad from FOSROC Super6 side Southern Knights, having previously enjoyed spells in the English Championship with London Scottish and Yorkshire Carnegie.
The prop has impressed in his outings for the Knights so far this season, including a two-try showing in January's win over Boroughmuir Bears.
The Scottish-qualified prop moves to Welford Road as part of a swap deal with Cortes.