Bellis said she and Huylebroek had accepted and would be returning to New Zealand at the beginning of next month to give birth to their baby girl.
"We are so excited to return home and to be surrounded by family and friends at such a special time," she said.
"We want to thank New Zealanders for their overwhelming support. It has been stressful and your kind words and encouragement helped Jim and I immensely."
Bellis' situation has been seen to highlight the consequences of the country's overstretched MIQ system, which has been a huge part of the successful domestic fight against Covid-19 - but thousands of New Zealanders have missed out on a "lottery" to return.
Bellis' lawyer Tudor Clee, who is representing Bellis pro bono and has done so for dozens of others in similar situations, has said the emergency MIQ allocation does not cater specifically for pregnancies, and success is incredibly difficult - even in situations like Bellis' - unless legal and/or media pressure are applied.
From June 1 last year to today 219 emergency allocation applications involved a pregnancy, with 29 approved. Of those, 65 were declined and seven were still in process, including Bellis'.
There were 118 cancelled by the applicants or they were not processed because they were incomplete.
Meanwhile, from October 30, 2020, to January 23, MIQ processed 8863 completed emergency allocation applications and approved 5396.
Bellis' approval was granted based on the risk factor of their location, Afghanistan, rather than on the need for time-critical, scheduled treatment, which Bellis had been seeking.
"Unfortunately, the Government fails to recognise that a birth is not a scheduled event," she said. "Therefore, this does not address the lack of a pathway for other pregnant New Zealand citizens to rightfully give birth in their home country."
Bellis said she was "disappointed" with how the situation overall played out, and would "continue to challenge the New Zealand government to find a solution to border controls to keep New Zealanders at home and abroad safe and their rights respected".
The Prime Minister is to make an announcement tomorrow about plans to reopen New Zealand to the world. The Government has long signalled a phasing out of MIQ from the end of this month, after pushing the date back from mid-January after the emergence of Omicron.
Robertson said flight arrangements had been made alongside the MIQ voucher.
Officials at the Ministry of Business, Innovation and Employment had worked hard to support an outcome that allowed Bellis to return home, Robertson said.
"There are rules and criteria. There are many, many people trying to find their way back to New Zealand and I have enormous sympathy for people in a number of different situations.
"One of the hardest things during Covid-19 has been that people have not been able to come back for funerals, for weddings, for situations like the birth of children, that's incredibly tough.
"We've had our MIQ process in place for a very good reason. It has supported our public health response, it has avoided a number of deaths but that doesn't make it easy for people who are at the other end wanting to come back to New Zealand."
Earlier yesterday, Clee said Covid-19 Minister Chris Hipkins had breached the journalist's privacy by sharing personal details in a statement and they were considering legal options.
Hipkins declined to comment.
Although Bellis has had a huge amount of support there have been some critics, including Muzhgan Samarqandi, a former Afghani broadcaster, who in a column published by 1News said Bellis had "minimised" Taliban atrocities by saying the regime had given her "safe haven".
Bellis has previously said she was reluctant to go public with her plight in the first place, and did so because she felt she had a responsibility with platform to speak up for others who didn't.
