The retired teacher died in hospital on Saturday, Channel 4 said.
Leon and wife June were among the first couples to join Gogglebox, in which couples across Britain are filmed watching TV, upon its launch.
Channel 4 and production company Studio Lambert issued a statement on behalf of Leon's family paying tribute to his "unique personality and sharp wit".
"It is with a heavy heart that we announce the sad news that after a short illness Gogglebox's Leon Bernicoff passed away in hospital earlier today," the statement said.
"Leon and his wife June were the first members of the public to be cast for Gogglebox back in early 2013, and they soon grew to become much-loved voices during the course of the show's 10 series to date.
"Leon's unique personality and sharp wit endeared him to fans of the show, as he contributed fully to Gogglebox's reputation as a programme full of warm humour and unvarnished opinion.
"To those of us that knew him personally, Leon was a man of unwavering principles who exerted a distinct paternal presence both on and off screen. He will be dearly missed by the entire Gogglebox family; cast and crew."
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Bernicoff is survived by wife June, two daughters, sons-in-law and grandchildren.
A devoted Everton fan, he met June in 1955 with the couple marrying five years later.
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