Mrs Zaghari-Ratcliffe will return to her husband and seven-year-old daughter Gabriella, who plans to show her mother her new toys.
Richard Ratcliffe said that it was going to be the beginning of a new life.
Mr Ashoori’s family said they could now rebuild the foundations of their family with their cornerstone back in place.
In a statement, they hailed his release and return to the United Kingdom after five long years before thanking those who laboured to bring him home.
A second man, Morad Tahbaz, who has Iranian, UK and US nationality, has been freed from prison but is not yet allowed to leave Iran.
Speaking in the House of Commons, Foreign Secretary Liz Truss paid tribute to the amazing willpower and perseverance shown by Mrs Zaghari-Ratcliffe, Mr Ashoori, Mr Tahbaz and their families, saying the sufferings they endured must never happen again.
Liz Truss said ministers would keep working to ensure Mr Tahbaz’s freedom.
The government has said it also settled a deficit of nearly £400 million owed to Iran from the 1970s, with the fund’s ring-fenced exclusively for humanitarian pursuits.
Speaking in the Commons, Tulip Siddiq, Mrs Zaghari-Ratcliffe’s MP said she welcomed home Nazanin after six long years, and can now say to her daughter Gabriella that this time mummy was really coming home.
Paying tribute to Mr Ratcliffe, who watched from the public gallery with Gabriella. Tulip Siddiq said he’d really set the bar high for husbands in his efforts to ensure his wife’s release.
Cuddling his daughter, Gabriella, Mr Ratcliffe told journalists they would really believe the news when they saw ‘mummy’.
He said he wanted to thank people up and down the country for supporting his campaign for her release, which included a hunger strike last October.
He said that it had been such a cruel experience in some ways, but it had also been an exposure to such a level of kindness and care, and he said that this would be a chapter in their lives, but that there were many more chapters to come.
Speaking after hearing MPs speak in the House of Commons, he told the Press Association the family would be away for a couple of days convalescing, doctors and check-ups and so on.
He said on returning to their home, the first thing his wife wanted to do was sit down on the sofa, make a cup of tea, and just be in the living room together, and that he looked forward to pottering around the neighbourhood and being normal again.
So, why has Nazanin Zaghari-Ratcliffe been released now?
The fundamental explanation is that London-Tehran ties are better than they’ve been before, and the International Revolutionary Guard and Iran’s judiciary no longer feel they need Mrs Zaghari-Ratcliffe for leverage in relations with the United Kingdom.
She was just a diplomatic pawn held prisoner by the Iranian authorities to put pressure on London.
If Tehran wanted to make nice, they would treat her well, give her access to medical assistance, possibly increase the frequency of visits, maybe even allow her a temporary release from prison, but if Tehran wanted to wield pressure on London, then her conditions might deteriorate or privileges might be removed.
The UK paying the historic £400 million debt for tanks sold but not delivered will have made a tremendous difference, and for years, the Foreign, Commonwealth and Development Office (FCDO) proclaimed the two issues weren’t connected, but in practice, the Iranians made them one and the same problem.