Goodwill, who was in post for little more than six months after replacing Edward Timpson in the role last June, confirmed the news to his local newspaper.
Speaking to the Scarborough News, he said: "I was not shocked as these things happen and it looks like the Prime Minister is wanting to bring in some younger people.
"I have had a good run and I am very proud to have been the first Scarborough MP since the First World War to have served as a minister in government.
"The Prime Minister called me in this morning and complimented me on the job I had done and she has my full support going forward. Not just with regard to Brexit but also to her [legislative] programme."
Nadhim Zahawi has been announced as parliamentary under secretary of state at DfE, although it not yet clear whether he will replace Robert Goodwill as children's minister.
And schools minister Nick Gibb has confirmed that he is set to remain at the DfE.
Delighted to continue at the DfE. Thanks to teachers and the Government's reforms, standards are rising: 154,000 more 6-year-olds on track in reading this year; 1.9 million more pupils in good or outstanding schools; and double or triple science GCSE entries up from 63% to 91%.— Nick Gibb (@NickGibbUK) January 9, 2018