Zaghari-Ratcliffe and another British-Iranian dual citizen Anoush Ashoori, who was detained in Tehran in 2017, boarded a plane from Mehrabad International Airport after the deal was struck.
Omani state television said the pair had arrived in the capital Muscat following their release in Tehran.
Earlier, a video aired by Iran's Tasnim news agency, affiliated to the elite Revolutionary Guards, showed a woman dressed in black Iranian Islamic clothes, boarding a Royal Air Force of Oman aircraft.
A third dual citizen, Morad Tahbaz, is set to be released from prison on furlough shortly.
UK Prime Minister Boris Johnson, on a trip to the United Arab Emirates and Saudi Arabia on Wednesday, tweeted that he was pleased the two's "unfair detention" had ended.
"The UK has worked intensively to secure their release and I am delighted they will be reunited with their families and loved ones," he wrote.
The breakthrough came after extensive diplomacy that secured the release of the three and led to agreement to repay the debt in a way that complies with UK and international sanctions.
The UK agreed to pay Iran 393.8 million pounds ($A711.4 million), which will be ring-fenced so the money can only be used for humanitarian purposes.
The UK government declined to offer details of the arrangement.
While the UK has refused to acknowledge a link between the debt and the detention of the dual citizens, Zaghari-Ratcliffe's husband has been outspoken in arguing that Iran was holding her hostage to force the UK to pay.
The debt has been a sticking point in UK-Iranian relations for more than 40 years.
After the Islamic Revolution in 1979, the UK cancelled an agreement with the late Shah of Iran to sell the country more than 1500 Chieftain tanks.
Since the shah's government had paid in advance, the new Iranian government demanded repayment for the tanks that were never delivered.
The two countries have haggled over the debt ever since.
Iran's top diplomat Hossein Amirabdollahian on Wednesday said the UK had paid its debt a few day ago, denying any links between the payment of the debt and the release of the prisoners.
Hope for a deal had been growing since Tuesday, when the MP who represents Zaghari-Ratcliffe's hometown announced that Iranian authorities had returned her passport.
Responding to questions about the talks before the deal was announced, Foreign Secretary Liz Truss said the UK believed the debt was legitimate and the government had been looking for ways to pay it that would comply with international sanctions.
When asked whether the UK would consider paying with goods such as medical equipment, Truss told Sky News she could not comment.
Zaghari-Ratcliffe was taken into custody at Tehran's airport in April 2016 as she was returning home to UK after visiting family in Iran.
She was employed by the Thomson Reuters Foundation, the charitable arm of the news agency, but she was on holiday at the time of her arrest.
The 43-year-old mother was sentenced to five years in prison after she was convicted of plotting the overthrow of Iran's government, a charge that she, her supporters and rights groups deny.
She had been under house arrest at her parents' home in Tehran for the last two years.
Ashoori was detained in Tehran in August 2017.
He had been sentenced to 12 years in prison for alleged ties to Israel's Mossad intelligence agency, something long denied by his supporters and family.
Tahbaz, a UK-US conservationist of Iranian descent, was caught in a dragnet targeting environmental activists while visiting Iran in January 2018.
The 66-year-old served on the board of the Persian Heritage Wildlife Association, a prominent conservation group in Iran.
Iran convicted Tahbaz, along with seven other environmentalists including his colleagues, on charges of spying for the US.
He was sentenced to 10 years and taken to Evin Prison.
Zaghari-Ratcliffe's husband Richard said the long ordeal appeared to finally be over.
"It's just a relief, the idea that we can go back to being a normal family, that we don't have to keep fighting, that this long journey is almost over," he told Reuters outside his London home.
with reporting from AP
