Nazanin Zaghari-Ratcliffe is set to arrive at RAF Brize Norton on a government-chartered flight this evening, it has been reported.
According to Times transport correspondent Ben Clatworthy, the British-Iranian aid worker will arrive in the UK at 10.30pm on a private government-chartered flight from Muscat.
Fellow dual-national detainee Anoosheh Ashoori is also expected to be on the flight.
Local MP Tulip Siddiq tweeted a picture of Zaghari-Ratcliffe in the air, saying she is “flying away from 6 years of hell in Iran”.
The announcement brings an end to a six-year ordeal for Mrs Zaghari-Ratcliffe who was arrested in 2016 in Tehran on spying charges – allegations she has always denied.
Mr Ashoori has been in prison for almost five years while Mr Tahbaz has been held for four.
Their release follows months of intensive diplomatic negotiations between London and Tehran.
Iranian state media said the UK has “settled a long-overdue debt” of around £400 million to Tehran.
It is understood the UK agreed to pay £393.8 million owed to Iran after it cancelled an order of Chieftain tanks following the overthrow of the Shah in the revolution of 1979.
Ms Truss tweeted: “I can confirm Nazanin Zaghari-Ratcliffe and Anoosheh Ashoori will return to the UK today, and Morad Tahbaz has been released from prison on furlough. They will be reunited with their families later today.”