Bruce, a Belgian Shepherd, and Blade, a German Shepherd, were euthanised after the prince completed his final shift as a search and rescue pilot at RAF Valley on Anglesey.
The Ministry of Defence confirmed the dogs had been put down, but described the timing as "entirely coincidence".
A spokesman said: "It is true two dogs have been put down, a couple of days after (Prince William left RAF Valley earlier this month). It was entirely coincidental."
He said the Prince did not work with the dogs, but they had been used to provide extra security at the base.
Bruce, who was aged nine, had "come to the end of his working life", while Blade "had a record of veterinary and behavioural issues" which meant the dog could not be reassigned to other duties, the spokesman said.
He said the department's policy is to "re-home all military working dogs at the end of their service life wherever practicable" and the decision for a dog to be put down is only ever "a last resort".