In a letter to the PM, she said she had lacked "transparency and openness". However, Labour has called on Mrs May to reveal as to when government officials knew about the undisclosed meetings. Ms Patel admitted unauthorised meetings with Israeli officials had "lacked transparency".
Priti Patel has resigned as international development secretary following controversy over her meetings with Israeli officials. The BBC's Diplomatic Correspondent, James Landale, explains how a family holiday went terribly wrong for her.
The row began last week, when the BBC revealed Ms Patel arranged a number of private meetings with business and political figures during a family holiday to Israel in August. After the visit, she asked her officials to look into whether Britain could support humanitarian operations conducted by the Israeli army in the occupied Golan Heights area. But Foreign Office officials strongly advised against this as the need for humanitarian aid was greater elsewhere and giving aid to the military broke aid rules, BBC diplomatic correspondent James Landale said.
Ms Patel resigned having been told by the prime minister to return from an official trip in Africa and report to Downing Street. It is the second cabinet resignation in the space of seven days, after Sir Michael Fallon quit as defence secretary last week. He was replaced by Gavin Williamson, as Mrs May adjusted her government team.
Ms Patel, who has served as the Tory MP for Witham in Essex since 2010, was formally reprimanded in Downing Street on Monday. She was asked to give details about the meetings, which were not sanctioned by the Foreign Office, and to correct information she initially gave when details of the meetings were published. It later emerged that she had held two further meetings in September with Israeli public security minister Gilad Erdan in Westminster and Israeli foreign ministry official Yuval Rotem in New York - again without government officials present.
Ms Patel's difficulties began last week, when the BBC revealed she had arranged a number of meetings with business and political figures during a family holiday to Israel in August, without telling Downing Street or the Foreign Office. It later emerged that after Ms Patel's visit to Israel, she asked her officials to look into whether Britain could support humanitarian operations conducted by the Israeli army in the occupied Golan Heights area.
A replacement for Ms Patel, who was a key figure in the Vote Leave campaign, was expected to be announced on Thursday, with a lot of attention on whether or not it goes to a Brexiteer.
Penny Mordaunt has been promoted to the cabinet as the new International Development Secretary, following the resignation of Priti Patel. Like Ms Patel, Ms Mordaunt was among Conservatives who backed Leave during the EU Referendum campaign. The former work and pensions minister, 44, has now left Downing Street and arrived at her new department.
It was the second cabinet resignation in a week. Last week Gavin Williamson replaced Sir Michael Fallon as defence secretary, after he quit saying his conduct had "fallen short" of the required standards after allegations of inappropriate sexual behavior.
Ms Mordaunt, MP for Portsmouth North, is a Royal Navy reservist and was appointed as the first female minister for the Armed Forces in 2015. It had been thought she was in the running to replace Sir Michael last week. She did not comment as she arrived at the Department for International Development on Thursday afternoon.
First elected to the Commons in 2010 she had been minister for disabled people in the Department for Work and Pensions until her promotion. She is also known for appearing on the reality TV programme Splash! in 2014.
As International Development Secretary she will be in charge of the UK's £13bn foreign aid budget.Ms Mordaunt would be a popular appointment within the party. She would keep the balance within the cabinet when it came to Brexit - in terms of the numbers of ministers who supported Leave or Remain during the referendum - as well as preserving the gender balance, an issue which Theresa May was concerned about.
Former Culture Secretary John Whittingdale told the BBC: "I think it's a good appointment. Penny is somebody who has a lot of experience, she has worked in an international department before - as armed forces minister, I have no doubt she will do an excellent job." Her Labour shadow Kate Osamor congratulated Ms Mordaunt on her appointment and said she "faces an immediate challenge of restoring integrity to British international development policy after the actions of Priti Patel".
That means she must unequivocally commit to the spirit, as well as the letter, of Britain's pledge to spend 0.7 per cent of national income on international development, and face down those in her party who want to merge DFID into the Foreign and Commonwealth Office
Asked if Ms Patel had been foolish or had made a concerted attempt at freelance foreign policy, the BBC's James Landale said: "I think it's pretty clear that the view within the government is there was an attempt to try to shape British policy within the Middle East."
Labor Party has now called on the government to set out what Foreign Office officials knew of the meetings. Writing to PM Mrs May, Labour's deputy leader Tom Watson said: "I have been informed that while she was in Israel, Ms Patel met officials from the British consulate general Jerusalem, but that the fact of this meeting has not been made public," he wrote. "If this were the case, then it would surely be impossible to sustain the claim that the Foreign and Commonwealth Office was not aware of Ms Patel's presence in Israel." He added: "The existence of such a meeting or meetings would call into question the official account of Ms Patel's behavior, and the purpose of her visit."
Middle East minister Alistair Burt told MPs on Tuesday that Foreign Office officials in Israel were made aware of Ms Patel's visit on 24 August and it was likely that her meetings had taken place beforehand.
Ms Patel was accused of breaching the ministerial code - which sets out the standards of conduct expected of government ministers. In her resignation letter, Ms Patel said: "While my actions were meant with the best of intentions, my actions also fell below the standards of transparency and openness that I have promoted and advocated. "I offer a fulsome apology to you and to the government for what has happened and offer my resignation."
In her reply, Mrs May said: ''As you know the UK and Israel are close allies, and it is right that we should work closely together. But that must be done formally, and through official channels. ''That is why, when we met on Monday I was glad to accept your apology and welcomed your clarification about your trip to Israel over the summer. "Now that further details have come to light it is right you have decided to resign.''
Conservative MP Jacob Rees-Mogg suggested disgruntled Remainers could be behind the leak that led to the downfall of Ms Patel, who is a prominent Brexiteer. He said that some people were "still very bitter" about the referendum result and "inevitably that colors their behavior".