Eru Tuari was the last witness giving evidence at the Auckland inquest into the brutal deaths of three-month-old Chris and Cru Kahui in 2006.
The twins died of head injuries in Auckland's Starship Hospital in 2006 and their father Chris Kahui was acquitted of their murders in May 2008.
Ms King was crying and upset when she told him she "did it", Tuari said.
He said he recorded part of the conversation on his mobile phone.
Tuari, who is currently serving a prison sentence, was reluctant to answer questions at first, but Coroner Garry Evans persuaded him that the inquest required his help.
Mr Evans granted suppression of Tuari's image today, but refused to suppress his name as he had previously given evidence in the High Court in Auckland during the trial without suppression.
Chris Kahui's defence claimed that the injuries were caused by Ms King, who denied that.
The hearing is expected to finish today.
