“He loved each and every one of us. We were blessed to have him,” Phumzile Langa said.
She described her father as a private man who loved to dance and sing.
“He was the one we ran to since our mother passed away. We felt safe with him. He was the one who loved us.”
She said she was thankful that God had blessed the family with him.
Hundreds of people gathered at the Durban city hall to pay their last respects to Langa.
President Jacob Zuma was expected to deliver a eulogy at the funeral.
Former chief justice Sandile Ngcobo, speaker of the National Assembly Max Sisulu and Chief Justice Mogoeng Mogoeng were also expected to deliver tributes.
Security was tight in and around the city hall, with scores of police keeping watch in the area.
Langa died last Wednesday at the age of 74. He had been in hospital for about a month due to a long illness.
He retired in 2009 and went on to chair the Press Freedom Commission, which looked into regulation of print media in South Africa.