Vilanova led the Catalan club for a season after taking over from Pep Guardiola, but was forced to resign last summer because of ill health.
Barca said in a statement: "The club expresses their deepest condolences over the passing of Tito Vilanova , who died today in Barcelona at the age of 45."
Vilanova, a former midfielder who spent his playing career largely in the Spanish second division, was Guardiola's assistant for four years at the Nou Camp, the pair having previously worked together with the B team.
He was first diagnosed with parotid gland cancer in November 2011 and the disease returned in December 2012.
He was away from the team between December and late March as he underwent surgery and treatment, but still won the La Liga title before resigning in July last year.
Barca sent their "deepest condolences" to Vilanova's family and said they would be opening a space in the main grandstand at the Nou Camp for people to express their condolences.
The club's president said on Twitter: "Tito Vilanova was a wonderful person, and will never be forgotten at FC Barcelona. Thank you for everything you taught us. Rest in peace."
Chelsea boss Jose Mourinho had several run-ins with Vilanova during his time in charge of Real Madrid, infamously poking him in the eye in one clash.
Mourinho said on Chelsea's Twitter account: "Tito Vilanova's passing is a sad day for football, for Barcelona and most importantly for his family and friends.
"On behalf of everybody at Chelsea Football Club I send my deepest condolences at this most difficult time."