Ms Zaghari-Ratcliffe was pictured going into 10 Downing Street with her family at lunch time on Friday.
A spokesman for the Prime Minister said: “We’ve said previously that the Prime Minister was open to meeting both Nazanin as well as Mr (Anoosheh) Ashoori.
“It is something we have been trying to arrange. I’ve set out that he is going to welcome her to Downing Street to discuss her ordeal in Iran.”
The official said the engagement was “something we’ve worked together on to make happen”.
The meeting will be the first time the two come face to face after Mr Johnson, then foreign secretary, wrongly claimed in 2017 that Mrs Zaghari-Ratlcliffe had been training journalists at the time of her arrest in 2016.
Four days later, she was summoned before an unscheduled court hearing, where his comments were cited as proof that she was engaged in “propaganda against the regime”.
Asked whether Mr Johnson would be apologising to Ms Zaghari-Ratcliffe, the spokesman replied: “I think it is important to remember that it was the Iranian government who were responsible for her unfair detention, and the decision to release her was always in their gift.
“However, I would point back to the Prime Minister’s words, his answers to questions on this before and he has previously apologised for his comments in 2017.”
Mrs Zaghari-Ratcliffe was freed in March along with fellow detainee Anoosheh Ashoori after the UK agreed to settle a historic £400 million debt dating to the 1970s.
“I was pleased to be invited to Number 10 along with my constituent Nazanin Zaghari-Ratcliffe and her family. I know her seven-year-old daughter Gabriella was particularly excited to be meeting the Prime Minister” Ms Siddiq, the constituency MP for Mrs Zaghari-Ratcliffe, said.
“After six long years of unjust and unlawful imprisonment in Iran, Nazanin deserves to hear directly from the Prime Minister about why it took so long to get her home.”
The continued detention of other British citizens, including Morad Tahbaz, will also be raised at the meeting, the MP said.
“(The Prime Minister) has a responsibility to ensure that others do not have to endure the six years of torment that Nazanin was put through,” she said.
“I will also be submitting evidence to the Foreign Affairs Committee’s inquiry on hostage taking, which I hope will get the bottom of the Government’s abject failure in handling cases like Nazanin’s.
“Never again must the Government allow British citizens to be taken hostage with so little done to secure their release and so few reprisals for those responsible.”
It comes after an announcement last month that MPs are to stage an inquiry into the detention and release from Iran of Mrs Zaghari-Ratcliffe and Mr Ashoori.
The Commons Foreign Committee said it would take evidence on how their cases were handled by British officials as part of a wider investigation into “state level hostage situations”.
Following their return both have been critical of the failure of the Foreign Office (FCDO) to secure their freedom sooner.
Announcing the inquiry, committee chairman Tom Tugendhat MP said their return was “long overdue” and that they were right to seek answers as to what happened.