says that Zarin, who battled cancer, died Saturday surrounded by his family.
"There are no words to describe how heartbroken we are," the statement read. "Thank you, everyone, for all your love and support during this difficult time."
His stepdaughter, Ally Shapiro, paid tribute to him on her Instagram account.
"You fought with dignity and courage, surrounded by all of us with love and respect till the very end," read the caption of a photo she posted, which showed her as a child with a much younger Zarin. "You can rest In peace now, we love you so much."
"Real Housewives" producer Andy Cohen tweeted: "I always enjoyed Bobby Zarin and admired his cool presence and steady hand."
Bravo, which aired the show, offered condolences. In a statement published on its website
, the network told the family that "our hearts are with you all."
The Zarins rose to fame after Jill Zarin was cast on the series. She appeared for the first four seasons. "Real Housewives" often highlighted their partnership and loving relationship; they ran a designer fabric store called Zarin Fabrics.
Zarin thought he had beaten thyroid cancer in 2009, according to People, but the disease returned four years later and settled in his lungs.
"The radioactive iodine usually kills off whatever undetectable cancer cells are left in your body after surgery," Zarin told People in 2015
. "We thought it was cured -- and it usually is in about 93 percent of cases. But I wasn't able to absorb the radioactive iodine. So it came back."
According to People
, Zarin underwent surgery to remove more tumors over the years. In July 2017, he was hospitalized for complications relating to his cancer.
The couple celebrated their 18th wedding anniversary earlier this month.
"Happy 18th! Anniversary to the love of my life Bobby Zarin," she wrote. "Bobby is the most perfect man I know. He never loses anything, never forgets anything and when I think he is wrong... he is always right!"
Zarin is survived by his wife and children David, Jennifer and Jonathan, along with his stepdaughter and grandchildren. There will be a public funeral service Monday at 10 a.m. at Riverside Memorial Chapel in New York City, a family representative told CNN.