Thousands of mourners turned out to pay their last respects to the former manager of the Glasgow club, who died at home last Thursday aged 51.
The former Scotland international, who was also a long-serving Celtic player and most recently the team's first-team coach and head of youth, died after losing a battle with cancer.
Mourners began arriving two hours before the requiem mass at St Mary's church in the Calton area of Glasgow.
Hundreds of fans were in the street outside the church from early morning and up to 3,000 had gathered by midday at Celtic Park where the service was being broadcast.
Stars of the football world arrived at the church throughout the morning.
Celtic boss Gordon Strachan arrived with the first-team squad to loud applause from those outside the church.
Others arriving included Rangers boss Walter Smith and captain Barry Ferguson.
Floral tributes were laid outside the entrance to the church and Celtic scarves hung from the railings.
The coffin was carried into St Mary's by Burns' former Celtic team-mates Danny McGrain, Peter Grant, Pat Bonnar and George McCluskey.
Rangers manager Smith and his assistant Ally McCoist, who were part of the Scotland international coaching set-up with Burns, were also among the pall-bearers.
In a eulogy, former Celtic team-mate Billy Stark described Burns as a "unique and special man".