"I'm delighted to have been appointed by the Prime Minister to be the new Secretary of State for International Development," the Independent quoted Mordaunt as saying.
"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," she added.
Earlier, Patel resigned under pressure after she broke protocol to meet politicians, including Israeli Prime Minister Benjamin Netanyahu, without informing Downing Street, while on a family holiday.
In her resignation, Patel apologised and said her actions "fell below the standards of transparency and openness that I have promoted and advocated".
Patel iswithinhe second cabinet minister to leave the government in a week after Sir Michael Fallon quit as defence secretary.
The Brexit-backing Minister was appointed as a Parliamentary Under-Secretary of State at the Department for Communities and Local Government in July 2014.
In May 2015, she was made minister of state for the Armed Forces at the Ministry of Defence (MoD), becoming the first woman to take this post.