The former Treasury minister takes over from Michael Gove, who is to become the government’s Chief Whip with responsibility for Conservative Party discipline in the run-up to the 2015 general election.
As well as running the Department for Education, Morgan will retain her women and equalities ministerial portfolio, which she took up in April.
Her previous government roles have included a junior ministerial role assisting universities and science minister David Willetts, who is also leaving the government as part of the reshuffle. She is also a former assistant government whip.
Morgan has been Conservative MP for Loughborough since 2010 and is a qualified solicitor. She has a parliamentary majority of 3,744 votes.
Elizabeth Truss is also departing from the DfE after two years as childcare minister. She has been promoted to Secretary of State for Environment, Food and Rural Affairs, replacing Owen Patterson.
The reshuffle has also seen Nick Hurd stand down as minister for civil society at the Cabinet Office. Hurd, who had held the post for four years, had also been responsible for youth services since its transfer to the Cabinet Office in July 2013.
Nick Boles moves from the Department for Communities and Local Government to become minister of state across the DfE and Department for Business, Innovation and Skills.
Gove’s departure as Education Secretary has been widely welcomed by teaching unions, many of which have clashed with him over education policy since his appointment in May 2010.
Dr Mary Bousted, the Association of Teachers and Lecturers (ATL) general secretary, said: “David Cameron has, belatedly, realised that Michael Gove’s ideological drive is no substitute for measured, pragmatic reform of the education system.
“Time after time he has chased newspaper headlines rather than engage with teachers. The dismantling of the structures which support schools, the antagonism which he displayed to the teaching profession and the increasing evidence of chaos in the bodies he established, in particular the Education Funding Agency, has led Cameron to one conclusion - Gove is more of a liability than an asset.
“Successful education systems value the views of the teaching profession, which Gove insulted when he called them ‘the blob’. ATL looks forward to a more constructive relationship with his successor, Nicky Morgan.”
Education union Voice described the changes at the DfE as “an opportunity for a fresh start”.
General secretary Deborah Lawson said: “Both Michael Gove and Elizabeth Truss were notorious for failing to listen to the views of education and early years professionals. Regardless of the weight of evidence presented to them, they would follow their own agenda, often denouncing those who held a different view as ‘the enemy’, ‘misguided’ and so forth.
“As a consequence, Michael Gove was the most divisive and unpopular Education Secretary for a generation.
“We hope that the new Secretary of State and her team of ministers, both new and ongoing, will be more receptive to the views of professionals and those who represent them, and will work with them to develop policies instead of imposing policies to be implemented.”
Chris Keates, general secretary of teachers union the NASUWT, said: “Whilst some may celebrate the departure of Michael Gove from the office of Secretary of State, the issue for the education service, for teachers, pupils and the general public is not a change of Secretary of State, but a change of policy.”
Elsewhere, Justice minister Jeremy Wright, who had been responsible for youth justice, has been promoted to Attorney General.
Iain Duncan Smith is to remain as Work and Pensions Secretary.