Ms Henderson was diving at the notorious Prestonhill quarry in Inverkeithing on Sunday when she failed to resurface.
Her body was recovered on Monday morning from the water.
The mother-of-one was a respected teacher at the public school in the capital.
Heriot’s principal Cameron Wyllie said: “Ms Henderson was an immensely talented, compassionate and vibrant person who loved teaching drama.
“She inspired a love of her subject in many young people over the years. Those of us at school are very shocked.”
Inquiries into the full circumstances are going and Ms Henderson’s death is currently being treated as unexplained. A report will be submitted to the Procurator Fiscal.
Inspector Ian Stephen of Dalgety Bay police station said: “This is a tragic incident and our thoughts are with Kelda’s family and friends as they come to terms with this terrible loss.
“We are supporting Kelda’s family at this time through specially trained officers.
“Inquiries are ongoing to establish the full circumstances surrounding this incident. I would like to thank the officers, public and partner agencies who assisted with our search.
There have been a number of fatalities at the quarry in the last few years with 18-year-old John McKay, drowning in the quarry in 2015.
Cameron Lancaster, also 18, was killed when he jumped into the quarry in 2014.