The burial marked the end of a week of memorial events for Mandela which have attracted thousands of South Africans and world leaders.
Addressing the congregation, South African president Jacob Zuma said: "It is the end of an extraordinary journey that began 95 years ago.
"It is the end of 95 glorious years, of a freedom fighter, a dedicated and humble servant of the people of South Africa.
"Fountain of wisdom, a pillar of strength, and a beacon of hope for all those fighting for a just and equitable world order. Your long walk to freedom has ended in a physical sense.
"Our own journey continues. We have to continue working to build the kind of society you worked tirelessly to construct. South Africa will continue to rise."
Prince Charles represented the Queen after Buckingham Palace confirmed the 87-year-old monarch would not make the journey to South Africa for the ceremonies to mark Mandela's death.
After the former statesman's death, Charles described Mandela as the "embodiment of courage and reconciliation" and said his passing had left "an immense void" in the lives of everyone who had been affected by his fight for justice and freedom.
The South African and Union flags were being flown at half-mast above 10 Downing Street to mark the ceremony.
Preparations for Mandela's funeral were marred by a public spat between the South African government and retired archbishop Desmond Tutu, one of the most prominent survivors in the long anti-apartheid struggle.
Mr Tutu, a Nobel laureate who has strongly criticised the current government, attended the service after earlier saying he would not, despite wanting to pay respects to his long-time friend.
He had said he was not invited - an apparent snub the South African government denied.