Venglos made history as the first manager from outside the UK and Ireland to take charge of a club in the English First Division when he was appointed Aston Villa boss in 1990.
He spent just one disappointing season in charge and went on to manage Celtic during the 1998-99 campaign, while his career also included spells in charge of the Czechoslovakia and Slovakia national teams.
A statement on the Celtic website read: "Everyone at Celtic is extremely saddened to hear of the passing of our former manager, Dr Jozef Venglos, who has died at the age of 84.
"The thoughts and prayers of everyone at Celtic are with Dr Jozef Venglos' family and the whole of football in Slovakia at this very sad time."
While Venglos' time with Villa was not successful, with the side finishing 17th in the First Division, having finished the previous season under Graham Taylor as runners-up to Liverpool, it had wider significance in paving the way for the influx of foreign managers.
Stan Collymore, who played for Villa from 1997 to 2000, wrote on Twitter: "Sad news that Dr Jo Venglos has passed away.
"First ever foreign manager to manage in the English top flight with Villa, didn't last long but always came across as a decent man. Rest in peace, Dr Jo."
Venglos' sole season at Celtic ended without silverware as Rangers claimed the title, but he is fondly remembered by Celtic fans for a 5-1 victory over their Old Firm rivals.
His most successful spells came with the Czechoslovakia national team. As assistant to Vaclav Jezek he won the 1976 European Championships before moving into the hotseat himself two years later and leading the country to a third-placed finish at the next tournament.
He also made the quarter-finals of the 1990 World Cup in a second spell in charge, while he became the first manger of Slovakia after independence when he was appointed in 1993.
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