The news was confirmed officially by team boss Vijay Mallya on Monday.
"I'm pleased to confirm that we've signed James as our third driver," he said.
Mallya said Calado, who is managed by Nicolas Todt, will drive on Friday morning at Monza, and also in initial practice "at several other races this year".
"It's always useful to get another driver's feedback on the car and it will help us evaluate James," he added.
Force India's current race drivers are Paul di Resta and Adrian Sutil.