Jane and Martin Weekes lost their toddlers Lillie, Jackson and Willsher in a blaze at Doha's Villagio mall in May 2012 that killed 19 people, including 13 children who were at a childcare centre used by expatriates.
Martin said the twins, a girl called Poppy and a boy named Parker, were born by Cesarean section yesterday morning in Auckland, where the couple set up home after the tragedy.
He said the mother and babies, who were born at 36 weeks, were in good health.
The twins were conceived through IVF following the death of the two-year-old triplets, though Martin Weekes said there was nothing that could "fill the void" left by the children who were killed.
"The twins are just another addition to our family," he said. "The sad thing is that Lillie, Jackson and Willsher weren't there to greet them."
A Qatari court in June sentenced five people to six years jail for negligence over the blaze, which broke out next to the unlicensed Gympanzee nursery and was blamed on an electrical fault.