British-Iranian nationals Nazanin Zaghari-Ratcliffe and Anoosheh Ashoori will be reunited with their families in the UK after being freed from Iran.
Mrs Zaghari-Ratcliffe will return to her husband and seven-year-old daughter Gabriella - who plans to show her mother her new toys.
"It's going to be the beginning of a new life," Richard Ratcliffe said.
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 UK after "five long years" before thanking those who worked to bring him home.
Speaking in the House of Commons, Foreign Secretary Liz Truss paid tribute to the "incredible resolve and determination" shown by Mrs Zaghari-Ratcliffe, Mr Ashoori, Mr Tahbaz and their families, saying the "agonies" they endured "must never happen again".
The government has said it also settled a debt of almost £400m owed to Iran from the 1970s, with the funds ring-fenced solely for humanitarian purposes.
Speaking in the Commons, Tulip Siddiq - Mrs Zaghari-Ratcliffe's MP - said: "Can I say to Nazanin, welcome home, after six long years. And can I say to Gabriella, this time mummy really is coming home."
Paying tribute to Mr Ratcliffe, who watched from the public gallery, Ms Siddiq said he had "really set the bar high for husbands" in his efforts to secure his wife's release.
Mrs Zaghari-Ratcliffe had been held in Iran since 2016 - accused of plotting to overthrow Iran's government, which she denied.
Mr Ashoori was arrested in 2017 and accused of spying, a claim he denied.
Morad Tahbaz, who has Iranian, UK and US nationality, has been released from prison but is not yet allowed to leave Iran, Ms Truss said.
She added that ministers would keep working to secure his 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.
"Ours has been a cruel experience in some ways, but it's also been an exposure to such a level of kindness and care," he said.
"This will be a chapter in our lives, but there are many more chapters to come."
Mrs Zaghari-Ratcliffe had been under house arrest and was given her UK passport back this week.
Mrs Zaghari-Ratcliffe and Mr Ashoori were flown from Tehran to the capital of Oman, Muscat.
Oman's foreign minister Badr Albusaidi tweeted a picture of Mrs Zaghari-Ratcliffe arriving in the country with Mr Ashoori, saying they would "soon" be with their loved ones in the UK.
Earlier, Ms Siddiq tweeted a picture of Mrs Zaghari-Ratcliffe, saying that she was in the air, "flying away from six years of hell in Iran."
"My heart goes out to Gabriella and Richard as her long journey back home to them gets closer by the minute," she added.
Antonio Zappulla, chief executive of the Thomson Reuters Foundation where Mrs Zaghari-Ratcliffe worked as a project manager, said staff were "overjoyed" at news of her release.
He said she had endured "utterly inhumane treatment" over the past six years, including being "denied her freedoms, separated from her husband and young child, battling significant illness, thrown in solitary confinement".
But he added that her freedom was "a ray of light and hope" at a time when the world was "in turmoil and the news has been consistently bleak".
Ms Truss told MPs the suffering of Mrs Zaghari-Ratcliffe and Mr Ashoori had "moved us all, and so does the prospect of them being reunited with their loved ones once again after this long and cruel separation".
Prime Minister Boris Johnson said he was "delighted" the pair could be reunited with their families after years of detention.
A £393.8m debt relating to a cancelled order for 1,500 Chieftain tanks dating back to the 1970s had been linked to the continued detention of Mrs Zaghari-Ratcliffe and other UK-Iranian dual nationals held in the country - although the government had previously said the two issues should not be connected.
Ms Truss told the BBC on Wednesday the debt was "legitimate" and that the government was looking for ways to pay it.
Labour leader Sir Keir Starmer said it was "an incredible moment" for Mrs Zaghari-Ratcliffe and her family after an "unimaginable ordeal".
He added that there would be questions to be answered about "what happened along the way", but at present his thoughts were with the family.