The former Manchester United and Juventus signed with ASM on Saturday as a free in an emotional moment.
Pogba is making his comeback after serving an 18-month doping ban and also surviving a blackmail plot.
Reflecting on his first hours with his new club, he told Monaco's official media channels: " Despite the experience, until I put on the jersey, the shorts...
"My hands are really sweaty! It's a positive stress, it's as if you had signed as a hopeful, you leave your family to go to the training centre.
"That's a bit what I felt."
Pogba continued: "There has always been talent here.
"Young Pat (Vieira), Thierry Henry, Yaya Touré, Jérôme Rothen, Adebayor, Trezegoal (David Trezeguet), Bernardo Silva, Thomas Lemar, Gallardo, Giuly, Morientes, Djorkaeff, Marco Simone, Fabien Barthez, there are some who have been here! Didier Deschamps too..."