The Manchester United boss, a long-standing friend, will deliver the eulogy during the 10am service at Christ the King Church, in King's Park.
The Irishman passed away last Friday at the age of 90 after a lifetime devoted to the Glasgow club as player, captain, coach and assistant manager.
Mourners are expected to include some of the Lisbon Lions players he brought to the club, including Billy McNeill and Bertie Auld as well as Kenny Dalglish, and current team boss Neil Lennon and his squad.
The Mass will be led by family friend Father Desmond Keegan, of the Redemptorists order of missionary priests.
The pair became friends, when both families attended the church in the 1970s. In later years the pair played golf together.
Fallon is survived by wife Myra and children Marie-Therese, Louise, Collette, Siobhan, Sean and Sinead.
His son Sean will also pay tribute to his father during the service.
Hundreds of mourners are expected to attend the funeral including footballers, supporters, relatives and family friends.
The hall of the church is being opened because of the high numbers expected, with screens showing a relay of the service.
After the mass a private burial will take place at Philipshill Cemetery, East Kilbride.
Fallon's association with Celtic spanned seven decades, from signing as a player in 1950 to receiving an emotional reception when unfurling the League flag over Celtic Park earlier this season.