Rimsha Masih's case attracted international attention on Pakistan's harsh blasphemy laws following her arrest in August in Islamabad.
She was accused of burning pages of the Qur'an as fuel for cooking, but a Muslim cleric was later accused of fabricating evidence.
Masih, who had been held in jail, was acquitted but her family was forced into hiding fearing vigilante justice.
Immigration Minister Jason Kenney said he'd been following the case and was prompted to act when a Pakistani contact asked him in January whether the family could come to Canada.
"I said absolutely, if they could get her out," Kenney said in an interview with The Canadian Press on Sunday.
"So a number of people did some very dangerous, delicate work to extricate her and her family from Pakistan and we provided the necessary visas."
Kenney issued what's known as a ministerial permit in order to facilitate their arrival.
He said he has now instructed immigration officials to process their applications for permanent residency under humanitarian and compassionate grounds.
The girl had been facing threats and was moving constantly, said a Muslim cleric who lobbied on the girl's behalf.
"I am sad that this innocent girl had to leave Pakistan. She had been acquitted by the court, and despite that it was not possible for her to live freely," Tahir Mehmood Ashrafi said.
It's rare for Kenney to comment on individual immigration cases and his department had previously refused to confirm whether the family was in Canada, citing privacy concerns.
But he said family members gave their consent to have their story made public after a blog post reporting on their arrival subsequently drew international media attention.
Kenney said he met with the family in Toronto in April, a few weeks after they arrived.
The case had been under scrutiny in part because of the girl's young age and questions about her mental abilities.
An official medical report at the time put her age at 14 although some of her supporters said she was as young as 11. The medical report also said her mental state did not correspond with her age.
Kenney said it was clear the girl does have some intellectual disabilities but her siblings are quickly adapting to their new life in Canada.
"There's a language barrier, but in any event, I could clearly see their profound gratitude for having received Canada's protection," he said.
Kenney said the cost of bringing the family over and resettling them was taken on by the International Christian Voice, a Toronto-based rights organization.
The group is run by Peter Bhatti, whose older brother Shahbaz was Pakistan's minister of minorities before being assassinated in March 2011.
Bhatti's death is often cited as a key influence on the Conservative government's decision to set up an office for religious freedom under the auspices of the Foreign Affairs department.
Kenney said, however, that Canada's ambassador for religious freedom was not involved in the family's case as he was appointed after the wheels had been set in motion.
Rescuing those facing religious persecution around the world has become a major theme of the government's efforts to resettle large groups of refugees.
Among them are Christians fleeing Iran and Iraq; an program to take-in some 20,000 Iraqis by 2015 is the largest single commitment to resettle a refugee population in more than 25 years.
But Kenney said resettlement efforts aren't limited to a single faith and are reflective of a broader government commitment to religious freedom.
"When states or unruly mobs seek to persecute or even kill people simply on the grounds of their fundamental beliefs, I can't think of a more obvious reason why a country like Canada should be available as a land of protection and a voice for the voiceless," said Kenney.
- with files from The Associated Press
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