Arriving on Sunday, December 17, the in-laws will get behind hundreds of locals engaged in the search.
Rock, who responded only to Spanish commands, went missing from his family's enclosed Paraparaumu Beach yard early last month.
His family, who describe him as like a child, said he was likely overwhelmed with the new sights, sounds and smells.
"When we moved to New Zealand four years ago we already had a plan to bring him over and so rented a fully fenced, pet-friendly house.
"Finally, after lots of paperwork, examinations, blood tests, translations, quarantine and a lot of work in order to pay it all, Rock came home.
"We couldn't wait to have our family complete again."
According to animal experts who had been in touch with the pair, Rock may have gone into survival mode, hiding during the day and coming out at night.
"The community has been amazing and without its support, we wouldn't have found energy to arrive where we are."
In cases of believed sightings, the couple asked people to please take photos to help confirm whether it is him.
"Also, please save my phone number on their contacts, which is 021 139 4790. Many times people haven't had my phone number and have run home to get it. In 10 minutes he could be miles away."
According to the family, while Rock looks like a typical border collie, his distinctions include a black back, white mane and completely white front legs.
At the time of his disappearance, as well as being microchipped, Rock was wearing a black collar with his contact and dog registration details.
"We won't give up — he's just lost and needs us.
"All we want is to have our beloved Rock back home."
For more information, visit the Come home Rock Facebook page.