The retired teacher and his wife June were one of the first couples to join the show's cast when it launched in 2013.
He died in hospital on Saturday, Channel 4 and production company Studio Lambert said in a statement issued on behalf of his family.
They paid tribute to the television favourite's "unique personality and sharp wit".
A devoted Everton fan, Bernicoff met June in 1955 with the couple marrying five years later.
During his run on the programme - which shows families across Britain watching television - he once described Nigel Farage as a "d***head".
Channel 4 and Studio Lambert said: "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.
"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."