Mr Tahbaz, a 68-year-old wildlife conservationist born in Hammersmith, has been released as part of a controversial prisoner swap involving the unfreezing by the Biden administration of $6bn (£4.8bn) of Iranian oil money.
The five prisoners, who also include US nationals Siamak Namazi and Emad Sharghi, had all been held on widely-criticised spying charges at Tehran’s infamous Evin prison.
They were taken from hotels in Tehran to a plane bound for Qatar, the first stage in a journey that would take them on flights to Washington.
Mr Tahbaz, co-founder of the Persian Wildlife Heritage Foundation (PWHF), had been detained in Evin Prison for over six years.
His wife, Vida, had also been placed under a travel ban by the Iranian authorities. She is also returning home to her family in the US.
The Tahbaz family said in a statement: “We are overjoyed and relieved to finally have Morad and Vida free and on their way back home after six years.
“We are very grateful to President Biden and his Administration for making this difficult but necessary decision to prioritise the lives of American citizens over politics.
“Thank you for leading with courage and compassion.
“At this time we are focused on the reunion of our family, the physical and mental health of Morad and Vida, and the path to recovery of these lost years.”
In January 2018, Iranian authorities arrested Mr Tahbaz and eight other people affiliated with the PWHF.
During his time in captivity, Mr Tahbaz had suffered health complications due to cancer, contracted Covid-19 twice, and completed a hunger strike.
Mr Tahbaz was left in Iran when the British-Iranian dual nationals Nazanin Zaghari-Ratcliffe and Anoosheh Ashoori were released in March 2022 as part of a deal negotiated by the then UK foreign secretary, Liz Truss.
Richard Ratcliffe, husband of Nazanin Zaghari-Ratcliffe, called the release a “happy beginning”.
“We are obviously delighted for all the families coming home,” Mr Ratcliffe told LondonWorld.
“Some I campaigned for for a number of years, and Nazanin knew them closely.
“It has been a long, long time. You think of it as a happy ending, but actually it is a happy beginning.
“They get a chance to be happy again, though it will take time to step out of battle mode.
“It is obviously really tough for the families left behind. Many of us have experience of that happening.
“And I hope the US has some assurances to keep them safe. There’s a couple of cases where I really worry.”
Mehran Raoof, a British-Iranian national and a labour rights activist, is still being detained in Tehran’s Evin prison after Revolutionary Guards agents arrested him in October 2020.
The US has said its citizens were imprisoned on baseless charges for use as political leverage.
In the first indication a deal was reached, they were moved in mid-August from Evin to a safe house in Tehran.
Five Iranians imprisoned in US jails, mainly on charges of violating US sanctions, are also being granted clemency as part of this swap. Not all of them are expected to return to Iran.
They have been named by Iran as Reza Sarhangpour, Kambiz Attar Kashani, Kaveh Lotfolah Afrasiabi, Mehrdad Moein Ansari and Amin Hasanzadeh.
The Prime Minister’s official spokesman said: “The Prime Minister is extremely pleased that Morad Tahbaz’s terrible ordeal is finally over and that he will be reunited with his loved ones.
“By seeking to use foreign nationals as bargaining chips, the regime’s leaders are fatally undermining Iran’s credibility on the world stage. They must stop using foreign nationals for political bargaining.
“In terms of the UK’s involvement, we weren’t a part of the negotiations between the US and Iran.”