Mr Dixon's passing was a reminder life was a precious gift to be embraced with arms outstretched every second of every day, friend Andrew Dwyer told mourners at St Patrick's Cathedral.
Mr Dixon passed away aged 89 earlier in July.
"Brian's passion drove him to great heights, on the field, in politics and in his life of service," Mr Dwyer said.
In a VFL career that began in 1952, Mr Dixon played 252 games for Melbourne Football Club, a record held until Robbie Flower broke it in 1987.
Mr Dixon's 18-year political career spanned portfolios including sport and recreation, employment and training, housing, social welfare and education, after entering Victorian parliament as the Liberal Party member for St Kilda in 1964.
His contributions included spearheading the 'Life. Be in it' exercise campaign and he was remembered for pushing for the introduction of compulsory seatbelt laws.
"Brian knew you only get one crack at the title," Mr Dwyer said.
"Brian led by example, and his legacy to us all is a simple message: Be in it today, live more of your life."
Championing the 'Life. Be in it' campaign was among Mr Dixon's proudest achievements, granddaughter Lara Nichols said on behalf of her mother Amy Dixon Riley.
"A deep thinker, a change-maker, a man with vision, and a seemingly endless supply of energy. That was my dad."
Former Tasmanian premier and football player Ray Groom said Mr Dixon's years at Melbourne Football Club were among its most successful.
"Brian was a great teammate and a close friend for 60 years," Mr Groom said.
"And without a doubt, he was one of the very best players to ever play for the Demons."
Former Labor MP Barry Jones said politicians from across the aisle respected Dixon's vision, energy, courage and integrity.
"And to his family, you have lost a hero," Mr Jones said.
"We will never forget him."
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