Laura Jacques and Richard Remde spent £67,000 (€89,867) cloning Jacques’s much-loved boxer, Dylan, after he died last year with a brain tumour.
She took cells from Dylan and sent them to the South Korean Sooam Biotech Research Foundation, in Seoul, where his DNA was extracted to produce two identical puppies, named Chance and Shadow.
They will spend seven months in quarantine with the foundation, before the North Yorkshire couple can bring them home.
Meanwhile, the couple will make trips to visit the dogs.
Remde told Sky News: “The puppies are doing really well. It has been money well spent and we cannot wait to get them home.”
Sooam has created 700 dogs, despite criticism of pet cloning by a number of organisations, including the RSPCA.
The procedure, plus the trips to South Korea, will cost the couple over £70,000.
Jacques said: “Dylan was such a special dog — he was my first dog and I had him all through my 20s. We lost him unexpectedly. He was given six to 18 months to live. Within 19 days he died.
“We found out we could freeze DNA and that was our intention, but it turned out his cells weren’t strong enough, so we went ahead with the clone.”
Jacques wants her new dogs to have similar physical traits to Dylan, but not to have his personality.