Donelan is the third MP to carry out the role in as many months after Badenoch replaced Nadhim Zahawi in July, when he was appointed business minister in Boris Johnson's reshuffle.
Donelan became an MP for the Conservative Party in Chippenham, in Wiltshire, for the first time in 2015.
Within two months of entering parliament she was elected onto the House of Commons education select committee and remained a member until 2018, when she became a government whip.
During her time as an MP she has voted against lowering the voting age for young people from 18 to 16.
She retains her role as a government whip while covering for Badenoch.
While as an education select committee member she looked at issues including children's social care standards and Ofsted inspections.
She was opposed to leaving the European Union, voting remain in 2016, but has since backed the UK's proposed withdrawal, including keeping an option of leaving without a deal on the table.
As children's minister she will oversee issues related to children's social care, special educational needs and disabilities (SEND), childcare, safeguarding in schools and policy around disadvantaged pupils, such as pupil premium and free school meals.
She will also support education secretary Gavin Williamson on apprenticeship and skills issues, which he took as part of his remit when former skills minister Anne Milton resigned in July and was not replaced.
Among those to comment on Donelan's appointment is Adoption UK chief executive Sue Armstrong Brown.
She said: "Despite a change in minister, our priorities remain the same. I look forward to working with the minister to deliver meaningful change for adoptive families."