Martin McKeague wrote on Facebook: “Corrie is no longer missing.
“What we mean by this is that after looking at all of the facts and evidence we now know what happened to our son.
“We are certain he is somewhere in the Suffolk waste disposal system, but his remains are essentially irretrievable.”
Corrie McKeague was 23 years old when he vanished on a night out in Bury St Edmunds, Suffolk, on September 24 2016.
Police believe he climbed into a waste bin and was taken away by a refuse lorry.
He had been stationed at RAF Honington, around 10 miles from Bury St Edmunds.
No trace of him has been found, and police said in March that the investigation was being handed to a cold case squad.
His father Martin McKeague wrote that police came to visit the family in Scotland to review the facts of the investigation in detail in October last year and February this year.
The evidence presented to him was “as thorough as it was compelling”, he said, and that experts “concluded beyond any doubt that Corrie had ended up in the Suffolk waste disposal system”.
“Accepting that conclusion has clearly not been easy for the McKeague family in Scotland, nor anyone else,” he wrote.
He said the remaining areas were either “too toxic to search” or “so vast it could take years to do so”.
He added that his son’s disappearance had been an “unbelievable and horrific journey of grieve (sic) and acceptance for the McKeague family”.
He said there are plans for a memorial for Corrie in the future.
Join our Facebook group Our Edinburgh to share images and news from and around the Capital