Police removed the body on Wednesday and Gibbons had been kept informed of proceedings.
But when contacted by the Herald today, Gibbons said he was "pretty certain" it was his sister found at the scene.
"I am pretty certain it is my sister based on a description of the clothing and the location where she was found.
"It's an intensely sad and confusing time but we are relieved to have her back to celebrate her life and to light her a safe passage onward."
He praised Thames police and its search and rescue teams who stayed with Bunning overnight before she was airlifted out yesterday.
However, he said there were a few learnings to come out of his sister's death.
"Life is so precious and fragile so if anything good can come of this it's that people are reminded to take the time to tell their family and friends that they are loved and valued and to treat strangers kindly."
A post-mortem is expected to be carried out on Bunning's body today. The matter will then be investigated by the Coroner.