Mr Zahawi said on Twitter that it had been 'an honour to serve as Children's Minister' and thanked his 'brilliant team' at the Department for Education.
He has been appointed a parliamentary under-secretary of state in the Department for BEIS to work with the newly-appointed business secretary Andrea Leadsom.
It has not yet been confirmed who will replace Mr Zahawi as children and families minister.
Mr Zahawi, who has been MP for Stratford-upon-Avon since 2010, was appointed children's minister by Theresa May in January last year during a reshuffle, at the same time as Damian Hinds became education secretary.
As well as being the minister responsible for early years and childcare, his portfolio included adoption and fostering, children’s social care, special educational needs, safeguarding in schools, disadvantaged pupils, school food, delivery of the 30 hours and social mobility.
Before becoming an MP, Mr Zahawi founded pollsters YouGov in 2000 from an office in his garden shed.
On Wednesday the new prime minister Mr Johnson sacked Mr Hinds and appointed Gavin Williamson as education secretary.
Mr Johnson's brother Jo Johnson has been brought back into the DfE, working across two government departments, as universities minister, and also as a minister of state in BEIS.
Yesterday the prime minister also confirmed the re-appointment of Nick Gibb as schools minister in the DfE.
Anne Milton, the apprenticeships and skills minister in the DfE who resigned earlier this week, prior to the new prime minister taking office, has also yet to be replaced.