The family from Edinburgh had launched a petition against a Home Office decision to deport 83-year-old Mozaffar Saberi and his 73-year-old wife Rezvan Habibimarand.
Following a high-profile campaign against the move, the Home Office has now granted them leave to remain.
The couple's children and grandchildren are all British citizens based in Scotland.
They had complained that the deportation of the elderly couple would mean that their family would never see them again.
"I am delighted to advise that a few hours ago the Home Office confirmed they will be granting leave to remain in the UK to Mr Saberi and Mrs Habibimarand," said the couple's lawyer John Vassiliou.
"A letter has been sent by the Home Office to the First-tier Tribunal (Immigration and Asylum Chamber) requesting the court's permission for the pending appeal to be withdrawn.
"This will be actioned by the court in the next few days and thereafter the Home Office can proceed to issue visas to the couple."
The couple had been due to attend an appeal hearing on 25 February but that will now no longer be necessary.
The family's lawyer revealed the Home Office will now issue visas to the couple, renewable every two and a half years for the next 10 years. Thereafter, they can apply for indefinite leave to remain and, subsequently, full British citizenship.
Hoyland previously told Sky News the prospect of his elderly grandparents being sent back to their native Iran had been tearing his family apart.
The Edinburgh Rugby player, who has played four times for Scotland, was speaking after a petition gathered more than 125,000 signatures in support of his grandparents.
Both grandparents are Iranian nationals but have spent 40 years, on and off, in Edinburgh.
They have travelled back and forth on visitor visas but have been based in the city permanently since 2012. They applied for leave to remain but their application had been rejected by the Home Office.
The couple have four children, 11 grandchildren and one great-grandchild in Scotland.
Following the deportation decision being overturned, the pair issued a statement expressing their relief.
"We've been given the world, everything, words cannot express how happy and grateful we are not to be separated from and be able to still see our grandchildren and children," they said. "This is the best news. We would like to thank everybody who helped and supported us and gave us hope."
The family's grandchildren said: "We would like to thank everyone who has contributed in any way to supporting our cause.
"The support has been overwhelming and being able to know that our grandparents are being allowed to stay with us is an incredible feeling. We couldn't be happier, we can continue to share our lives and build memories with them for as long as possible."