Speaking on The Project, the Logie Award winner said he spent "half an hour laughing" before she "fell asleep and never woke up."
Despite the tragic situation, Johnson vowed that he continue his sister's legacy just hours after attending her funeral in Canberra.
"I will accelerate the push for a cure... I'm not going to stop, mate," he told the hosts.
"She was training her little brother to do her work when she was gone. I'm ready for that."
The two have worked tirelessly for years on Love Your sister charity which was set up to raise money for the Breast Cancer research.
Johnson also spoke about his sister's service and described it as 'beautiful' and went exactly as Connie had planned.
"Seems weird to apply the word 'perfect' to a funeral, but you know, it was perfect," he said.
An absolute inspiration. Sending love to the family during this difficult time.