"This news has left me heartbroken," the actress tells PEOPLE in a statement. "I can only imagine the pain his family feels at this time, and my heart goes out to them, especially Deborah, Michael and Liliana."
"I spent 10 years of my life studying and admiring one of the most brilliant actors, yes, but more importantly, one of the greatest men," Sigler, who played daughter Meadow Soprano on the hit HBO show, continues.
"Jim had the ability, unbeknownst to him, to make you feel like everything would be alright if he was around."
The pair were a central part of one of the series' strongest episodes, in which Gandolfini's Tony and Sigler's Meadow take a road trip to visit New England universities, culminating in Tony admitting his Mafia ties to his daughter before strangling an FBI informant with a wire.
"I treasure my memories with him and feel so honored that I was an up-close witness to his greatness," the actress adds.
Sigler, now 32, is engaged to Cutter Dykstra and expecting their son in August.