Gregg and Kathryn Brain had set up home in Dingwall in 2011 but last month they were advised to quit the UK voluntarily after the Home Office said their leave to remain would not be continued.
Their church had been helping with their appeal to stay.
Speaking to Premier earlier this year, Gregg said he believed God had called his family to the UK and he has brought them to this point.
He said: "It has been our experience that when we feel these sorts of callings that God has opened doors for us, not just in the eleventh hour but well and truly into the 59th minute."
It was confirmed on Tuesday that as Mrs Brain had been offered a job with a hotel group, the couple and their seven-year-old son Lachlan could stay.
A Home Office spokesperson said: "We have always been clear with the Brain family that if a suitable job offer was received an application to remain in the UK would be considered.
"We gave them a number of extensions on an exceptional basis to allow them to try to secure a job that would allow them to meet the immigration rules.
"Mrs Brain was subsequently offered a job with a hotel group. This has been considered and we are satisfied that it meets the conditions for a tier two visa.
"Today we have written to Mrs Brain and confirmed that she and her family have been granted leave to remain in the UK."
The family had initially moved to the UK on Mrs Brain's student visa but a two-year post-study visa scheme then on offer was later withdrawn by the UK Government.
Mr Brain has previously warned the family would be ''homeless, jobless and significantly in debt'' if they were not allowed to remain.
As part of their fight, they met Scottish First Minister Nicola Sturgeon, who pledged she would do everything in her power to help.
