Vialli was diagnosed with cancer in 2017 but was still able to play a significant role in Italy's European Championship title-winning campaign in 2021 assisting long-time Sampdoria strike partner and national coach Roberto Mancini.
However, the signs were not good when he announced a temporary leave from his role with the national team in December to focus on his health.
Vialli spent eight seasons at Genoa-based Sampdoria before joining Juventus in 1992 for a then world record 16.5 million euros.
He won the Champions League with Juventus before joining Chelsea in 1996 and becoming player-manager in 1998.
Vialli took over from the sacked Ruud Gullit late in the season, and went on to lead Chelsea to victory in the League Cup, UEFA Cup Winners' Cup and UEFA Super Cup.
He also guided Chelsea to victory in the 2000 FA Cup final but was sacked in the following season.
Chelsea's current co-owners Todd Boehly and Behdad Eghbali said in a statement: "This is truly an awful day for Chelsea Football Club. Gianluca's legend will live on at Stamford Bridge.
"His impact as a player, a coach and most importantly as a person, will be forever written across our club's history."
Sampdoria, where Vialli won the Serie A title and European Cup Winners' Cup, said in their statement: "We have come a long way together, growing and searching, winning and dreaming. You came as a boy, we salute you as a man."
Vialli played 59 times for Italy, scoring 16 goals.
The Italian football federation (FIGC) said a minute's silence would be held before all matches in the country this weekend.
"Gianluca was a wonderful person and leaves an unbridgeable void, in the national team and in all those who appreciated his extraordinary human qualities," it said.
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