The dogs were put down following Prince William's final shift as a search and rescue pilot at RAF Valley in Anglesey last week, 'The Sun' reported today.
The Ministry of Defence (MoD) said it always tried to rehome dogs and the timing was a coincidence.
Belgian shepherd Brus was at the end of his working life and Blade, a German shepherd, had "behavioural issues".
The duke started his training at RAF Valley in January 2009 and graduated as a search-and-rescue pilot in September 2010.
He announced he was to leave the military to focus on royal duties and charity work after carrying out his final operational shift on September 10 this year.
An MoD spokesman said: "It is true two dogs have been put down, a couple of days after. It was entirely coincidental."
He added that Blade, who also "had a record of veterinary issues", could not be reassigned to other duties.
"Unfortunately in this case the dogs were unsuitable for rehoming or alternative duties and so sadly, for the animals' welfare, they had to be put down.
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