Unicef, which arranged their treatment, said the twins flew back to Sanaa after an eight-hour operation and several months of recovery.
They were operated on at Al Takhasusi, a private hospital in Amman.
“I can’t express my feelings,” said the twins’ father Yasser Albukhaity.
“There was a feeling of fear at the beginning, but we had great faith in God and in the medical team.
“I wish for them [the twins] to be educated like other children, to finish their higher studies, and to be of great benefit for their country in the future.”
Jordan has in the past three decades become a centre for treating patients from Yemen, Iraq, Libya and other strife-ridden countries in the Middle East.
Unicef said private donations covered their medical expenses and transport.
The organisation's Yemen representative Philippe Duamelle said it was “a happy ending story” for a country that has little to celebrate.
“This is a welcome happy ending story of one family, but millions of children in Yemen continue to suffer in silence,” he said.
Yemen has been torn by civil war for the past seven years. It was one of the poorest countries in the world before the conflict.