The family added that they were "deeply touched" by the rescue efforts to find him. The 34-year-old from London disappeared on May 27 when he went on a trek to a waterfall on Tioman Island, off the southeastern coast of the country.
A body found on Wednesday has been confirmed to be Huntley's but the cause of death is not yet known.
In a statement, the family said: "We would like to thank everyone who came together in the last week to do everything in their power to help find Gareth.
"You have been extraordinary and we are deeply touched and deeply grateful."