The funeral mass was held in St John the Baptist Church in Ovens, Co Cork where Miller was baptised and confirmed and across the road from where he went to school.
Republic of Ireland manager Martin O'Neill, who was Celtic boss when the midfielder made his breakthrough into the first team in 2004, was also in attendance along with Miller's former Ireland manager Steve Staunton.
Along with Keane and O'Neill was Roy Keane and Martin O'Neill and Miller's former Ireland team-mate Kevin Doyle.
Miller died of cancer aged 36 on Friday.
Among the gifts brought to the altar during the mass were football jerseys and photos of his family.
Celtic players wore black armbands in Mr Miller's memory during their Scottish Cup victory over Partick Thistle on Saturday.
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The 28-year-old is a crucial part of the North's Games delegation led by Kim Yong Nam, North Korea's nominal head of state. Moon also urged North Korea to talk to the United States, his office said.
Ireland's assistant manager Roy Keane was among the sports fans, friends and neighbours who paid their respects to Liam and his family.
The 36-year-old Cork man, who began his distinguished footballing career with Cork City and also played for Manchester United, passed away in Marymount Hospice.
Former teammates Chris Sutton, John Hartson, Wayne Rooney and Rio Ferdinand have been also been paying tribute on social media.
The world of football was united in grief after news emerged of Liam's passing last week. Among them were a number of high-profile former Celtic staff and players.
President Michael D Higgins who said Liam "brought skill and passion to the game" is expected to be represented at tomorrow's funeral, as is Taoiseach Leo Varadkar.
O'Neill gave the player his Celtic debut, setting him up for a career that took in the likes of Manchester United, Leeds and Sunderland.
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Vicky was a nanny to Jeremy's three children with his ex-wife Carla Germaine - Alice, 14, Ava, 12, and eight-year-old Henry. Jeremy and Carla were granted a divorce in February 2016, with former model Carla citing "unreasonable behaviour".
"As president of Ireland I send my condolences to his family and friends, and to all those who love and support Irish sport and who will keenly feel his loss".
During the service the priest said: "Liam used his talents to the full and in so short a time".
Former Manchester United manager Alex Ferguson described Miller as "a good professional who served our club in an excellent manner".
Ahead of the funeral, Cork City manager John Caulfield encouraged local people to turn out in force as a show of support.
He was surrounded by family members, including his wife Clare, children Kory, Leo and Belle, his parents Billy and Bridie and siblings Sean, Robby, Martin and Suzanne.
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It warned against agreeing to talks before North Korea scrapped its nuclear program, saying it would only "benefit the enemy". Kim is now among her brother's top 20 officials and is seen as something of a gatekeeper to the leader, the analysts said.