Dinenage, who was elected to represent Gosport at the 2010 general election, was previously a joint DfE and Ministry of Justice minister, where she was a junior minister for family justice, but is now solely DfE.
She was named as a member of the DfE ministerial team last month alongside Edward Timpson, Robert Halfon, Nick Gibb, Jo Johnson, and Lord Nash, following a reshuffle by Prime Minister Theresa May.
She replaces Sam Gyimah, who was moved to the Ministry of Justice, as childcare minister. Responsibility for child and adolescent mental health services, which had previously been part of Gyimah's brief, has been handed to children's minister Edward Timpson.
Neil Leitch, chief executive of the Pre-school Learning Alliance, said: "We welcome the news that Ms Dinenage has been named as the new early years minister and congratulate her on her new role.
"With the planned rollout of the 30-hour free entitlement offer, the imminent launch of the government's early years workforce and life chances strategies, and the publication of a revised EYFS Framework, this is clearly a time of significant change and transition for the early years sector - and one that can only benefit from positive, honest and open relationship between the sector and government."
Concerns were previously raised over the amount of time taken to appoint a childcare minister.
The Professional Association for Childcare and Early Years (Pacey) said it welcomed the appointment of Dinenage. Liz Bayram, chief executive of Pacey, said issues within the sector requiring urgent attention include the implementation of the extension to the free early education entitlement and the development of a workforce strategy.
"All children benefit from high-quality early education and its vital the planned extension of free entitlement to 30 hours a week for working families does not place at risk the huge improvement in quality our sector has achieved in recent years," she said.
"High quality that has been achieved through the hard work and dedication of practitioners and settings, despite reduced funding and support levels from government."
She added that Pacey is pleased that environment minister Therese Coffey's role includes responsibility for rural childcare.
"Given so many registered childminders play such a critical role in sustaining rural childcare we will be seeking an early meeting with her to discuss how we can support this new brief for the Department for Environment Food and Rural Affairs"