By Hazel Shearing
British-Iranian nationals Nazanin Zaghari-Ratcliffe and Anoosheh Ashoori are on a plane leaving Iran after being freed, the government has said.
Mrs Zaghari-Ratcliffe will be reunited with her husband and seven-year-old daughter, who plans to show her mother new toys when she returns to the UK.
"It's going to be the beginning of a new life," Richard Ratcliffe said.
Boris Johnson said he was "delighted" the pair could be reunited with their families after years in detention.
The government said it had also settled a debt owed to Iran from the 1970s.
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.
A third dual national, Morad Tahbaz, has been released from prison but will not be returning to the UK, Foreign Secretary Liz Truss said.
She said 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 him going on 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.
Tulip Siddiq, Labour's MP for Hampstead and Kilburn, tweeted a picture of Mrs Zaghari-Ratcliffe and wrote: "Nazanin is now in the air flying away from 6 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.
Earlier, Ms Siddiq told the BBC Mrs Zaghari-Ratcliffe had been at the airport with her passport, but remained "under the control of the Iranian Revolutionary Guard".
"I won't rest until she is on British soil, in West Hampstead, in her house," she added.
Mrs Zaghari-Ratcliffe's sister-in-law Rebecca Ratcliffe told BBC News it was an "emotional day".
She said Mrs Zaghari-Ratcliffe had been picked up and taken to the airport with her parents, who were not allowed in a holding room with her because she was "still under Iranian control in the airport".
Earlier Ms Siddiq said Mrs Zaghari-Ratcliffe had been "dreaming" about the day she could return to the UK.
A £400m 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 has previously said the two issues should not be linked.
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.