It was standing room only at St Peter's Church as friends, family members and colleagues crammed inside for the service.
There were similar scenes outside on the piazza – where the service was shown live on a big screen – as a huge crowd began to form from 9.30am.
Watch today's funeral service courtesy of Wolverhampton Council
An immaculately-observed minute's silence took place prior to the service.
Dozens of dignitaries were present at the service to pay their respects.
They included the city's three MPs, Pat McFadden, Eleanor Smith and Emma Reynolds.
Ms Reynolds said: “This was a fitting tribute to Elias, who in his time touched the lives of so many people in Wolverhampton.”
Wolverhampton council was also heavily represented, with Mr Mattu's close friends' council leader Roger Lawrence and Councillor Pete Bilson both in attendance.
Councillor Lawrence, who delivered a touching eulogy at the service, described Mr Mattu as ‘loyal, courteous and wise’. “We will remember him with affection and with love,” he added.
In an emotional address, Mr Mattu's daughter Jessica said: "He was my heart, my protector, my dad. I am so proud of everything he accomplished and the man that he was."
She added: "You've left me, mom and the boys, but you are in a better place. We will miss you everyday."
His son, Ishmael Mattu, said: "You were the best dad who became my best friend as I grew into an adult."
In a nod to his father's weight-lifting past, he added: "We thought you were the strongest man in the world."
Mr Mattu’s brother, the Rev Ashok Masih Mattu, said: “Elias was a great man. I am very proud of my brother. He was a people’s champion.
“There will never be enough words to pay tribute to the wonderful man that he was.” Addressing the congregation, Rev David Wright described Mr Mattu as ‘a man of devout Christian faith who valued people of all faiths and none’."
The service also featured bible readings from councillors Sandra Samuels and Jacqueline Sweetman, as well as a rousing anthem from the Choir of St Peter’s Collegiate School.
Earlier, streets around the city came to a standstill as a funeral cortège, led by a horse drawn carriage, carried Mr Mattu's coffin from his home in Penn Fields.
Councillor Mattu died last month, aged 59, following a long battle with illness.
He served as a Labour councillor for Graiseley ward for nearly 18 years, having come to the city with his family from their native northern India as a nine year old.
Last May he was named Wolverhampton's 159th Mayor.
Educated at Graiseley School, Wulfrun College and Wednesbury College of Commerce and Technology, he then studied law at Wolverhampton University while volunteering at the Citizens Advice Bureau.
He was also a regional coach and referee, opening his own club in the late 1980s, training five British power-lifting champions and one European champion.
Mr Mattu's final resting place is at Danescourt Cemetery.
He leaves behind his wife Asha and children Anthony, Ishmael and Jessica.