Pope Francis was elected to lead the Catholic Church in 2013, replacing Pope Benedict XVI.
The 88-year-old was a known football fan and had supported Argentine side San Lorenzo since he was a child.
A tribute from the club read: “Our hearts ache. Pope Francis has left this world, but he will never leave our hearts.
“An honorary member of our club, his passion for San Lorenzo always moved us especially, and unites us in a constant prayer for his soul.
“He celebrated every achievement with us with enormous generosity, receiving the delegations that visited him in the Vatican during his papacy.”
A number of Serie A clubs also posted tributes to the Pope following his passing.
“A loss that deeply saddens our city and the entire world,” a Roma statement read.
“His faith, his humility, his courage and his dedication have touched the hearts of millions of people, making him a moral reference of our time.”