Ms Mordaunt was minister for disabled people before she received the call from Theresa May on Thursday inviting her to join the Cabinet.
She was brought across from her junior ministerial role after Ms Patel was forced to quit on Wednesday, having angered Ms May by failing to tell the Prime Minister she had held unofficial meetings with high-level Israeli politicians.
Asked if she was joining a Cabinet “in chaos”, Ms Mordaunt said: “I’m delighted to have been appointed by the Prime Minister to be the new Secretary of State for International Development.
“I’m looking forward to working with the team here to continue building a safer, more secure, more prosperous world for us all and really giving the British public pride in what we do.”
Ms Mordaunt, 44, has long been seen as a rising star in the party and was a prominent Brexiteer during the referendum campaign in 2016, going on to back Andrea Leadsom in the Tory leadership contest.
Her arrival will please Brexiteers who feared that Ms Patel’s demise would diminish the will of the Cabinet to drive EU withdrawal forward.
She was first elected to Parliament as MP for Portsmouth North in 2010, and achieved ministerial rank under David Cameron between 2014 and 2016 before being appointed minister for disabled people when Theresa May took power.
Ms Mordaunt become better known after appearing in the reality TV show Splash. She was criticised after she delivered a speech on poultry welfare in the Commons for the sole purpose of saying the word “c**k” several times after Royal Navy colleagues dared her to.
During the referendum campaign she clashed with Mr Cameron after incorrectly claiming the UK does not have a veto over the new membership of states such as Turkey – despite it being a key part of the Treaty of the European Union.
At the time Mr Cameron said the minister was “absolutely wrong” on the matter, and implied that it showed the judgement of the Leave-backing politicians on other matters should be called into question.
In other changes sparked by Ms Patel’s departure, Sarah Newton MP becomes minister for disabled people and Victoria Atkins MP becomes a junior minister at the Home Office.
It first emerged last Friday that Ms Patel had travelled to Israel over the summer and conducted a number of meetings and visits with Israeli officials and politicians.
During the 13-day visit, which she described as a “holiday” paid for by herself, she was accompanied in meetings by Lord Polak, president of Conservative Friends of Israel, and discussed departmental business with key figures including the Israeli Prime Minister Benjamin Netanyahu.
It triggered accusations that she had ignored ministerial rules that she should tell the Foreign Office about business taking place overseas, and embarrassed Ms May who was kept in the dark about it for months.
When the trips emerged Ms Patel initially told a reporter that Boris Johnson’s Foreign Office had been informed, but later admitted in a statement that it was not.
Ms Patel also publicly apologised and accepted that she had not acted in “accord with the usual procedures”, and was forced at a meeting with Ms May to set out all of the appointments she had in Israel, 12 in total.
Her public contrition appeared to have saved her political career, but over the next two days details of her trip and other meetings emerged that had not been shared with Ms May.
These included that she had discussed the idea of handing UK aid cash to the Israeli army to carry out humanitarian ops in the Golan Heights, that she had visited an Israeli field hospital there and that she had a further meeting with another Israeli minister, Gilad Erdan, in Westminster.
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