Morgan, until now Financial Secretary to the Treasury and Minister for Women, had her promotion broadcast on the Prime Minister's Twitter account. Gove has been nominated as Tory chief whip.
Morgan was first elected in 2010 and has climbed swiftly through the ranks of the Conservative Party. In addition to her new role, she will continue as Minister for Women and Equalities.
Gove has been a controversial figure throughout his tenure as Education Secretary, and BBC political editor Nick Robinson has said that many will view his new post as a demotion, as he is no longer a full cabinet member: "He now continues not as a leading Tory figure in his own right but as 'a friend of David and George.'"
Ofsted chief Sir Michael Wilshaw said he was "surprised and shocked" by the news: "I'm a great admirer of the Secretary of State, I think he's been a transformative and radical minister of education."
New data from Ofqual shows that schools and colleges across England are making progress in cyber security training, but are struggling to recover quickly from attacks when they occur.
Three schools have been fitted with solar panels over the summer as part of a government-funded scheme, with eight more schools set to get their solar panels this autumn.