Van Zandt played Silvio, the consigliere or right-hand man of Gandolfini's New Jersey mob boss Tony Soprano, for six seasons on the celebrated HBO show. Van Zandt's wife Maureen also played Silvio's spouse Gabriella on the series.
"I have lost a brother and a best friend. The world has lost one of the greatest actors of all time. Maureen and I send our deepest sympathy and love to Deborah, Michael, Lily, and all of Jimmy's family," Van Zandt said via Twitter.
Edie Falco, who played Tony's long-suffering wife Carmela, described Gandolfini in a statement as "a man of tremendous depth and sensitivity, with a kindness and generosity beyond words."
Steven Schirripa, who played Tony's brother-in-law Bobby tweeted: "Jimmy was a dear friend and like a brother to me. He was a great actor and a great father. I will miss him terribly. I am very sad."
Vincent Curatola, who played John "Johnny Sack" Sacramoni, told the New York Post, "I used to call him the 'Fearless Leader.'
"I was just coming off the ferry from Manhattan when I heard [he died] and I said, 'I hope this is a rumor.'
"We were together at Mohegan Sun [casino] in March and had a great time. I don't know what happened. [New Jersey Gov.] Chris Christie just called me and said, 'When they bring him home, we'll do whatever his family needs,' because he's a Jersey boy."