No trace of the 23-year-old has been found since he was last seen in Bury St Edmunds on September 24, 2016, and the current theory is that he climbed into a waste bin and was taken away by a bin lorry.
Detective Superintendent Katie Elliott said: "It is extremely disappointing that we have not been able to find Corrie. I can only imagine the strain Corrie's family have been under over the past 18 months and I thank them for their patience and understanding.
"Whilst the investigation has drawn to a natural conclusion we will continue to work with the family to provide answers to their questions and help them understand what may have happened.
"We have now reached a point where we are unable to make any further progress, and have gone as far as we realistically can with the information we have. If any new, credible and proportionate enquiries relating to Corrie's disappearance emerge we will pursue them."
Suffolk Constabulary said in a statement that investigators had been through all realistic possibilities in detail and that there was no evidence of foul play.
Police carried out two searches of a landfill site at Milton near Cambridge last year, with the first search lasting 20 weeks and the second, lasting seven weeks, concluding in December.
They sifted through thousands of tonnes of waste in the two areas where it was most likely for Mr McKeague to have ended up, but the records used were not detailed enough to rule out him being elsewhere.
Investigators were also initially given the wrong weight of the bin that Mr McKeague may have climbed in, making it too light to support the theory that he was in there. However this was later corrected, showing that it was actually much heavier than normal.
Mr McKeague's father Martin told the Daily Mirror he fears the airman may have killed himself.
Mr McKeague, 49, said he thought his son knew he was going to become a father which may have affected his mental state.
He said: "I just can't help thinking this would have weighed on him heavily and he may have actually chosen to get in that bin that night knowing what would happen.
"It's as probable as anything else and it makes it no less heartbreaking."
Assistant Chief Constable Simon Megicks said the inquiry had been reviewed by senior officers as well as external experts, and he had "absolute confidence in the way the investigation was conducted".