"With tremendous sadness we inform you of Michael's death", read the message from Robinson's family on his Twitter account.
"It leaves us with a great emptiness, but also countless memories, filled with the same love that you have shown for him".
After hanging up his boots in 1989, Robinson would go on to enjoy a successful career as a television presenter and commentator and gained widespread praise for his work in Spain, where he had settled with his family.
Robinson's one season at Liverpool, which also earned him a league title medal, was the peak of a career that included spells at Manchester City and Brighton, and 24 appearances for Ireland.
Liverpool also shared condolences with their former player's family and friends. You were the one who always made us happy about sport.
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Leicester-born Robinson was a member of the Liverpool team that won the 1983/84 European Champion Clubs' Cup, coming on as an extra-time substitute in the final against Roma at the Stadio Olimpico. "Rest in peace, Michael". "You'll never walk alone".
Robinson scored three times as the Republic of Ireland narrowly missed out on qualification for the 1982 World Cup, netting against Cyprus, the Netherlands and France.
Robinson was "a person who loved football and who knew how to explain it with knowledge and ingenuity", the Spanish champion said.
A former Liverpool striker, who was part of the club's famous treble-winning side in the early 1980s, has passed away at the age of 61.
"Thank you Michael Robinson".