There had been speculation overnight that Mr Gove would quit on Friday morning, after it was reported that he had refused an offer to become Brexit Secretary.
He left a meeting at Downing Street on Thursday night without making comment. It is understood that Mr Gove asked to be able to renegotiate Theresa May’s draft withdrawal deal as a condition for taking the job.
A source close to the Aberdeen-raised minister was quoted saying that Mr Gove "thinks it is important to continue working with Cabinet colleagues to ensure the best outcome for the country".
Taking part in a radio phone-in earlier as speculation mounted over Mr Gove’s future, the Prime Minister had said she wants all Cabinet ministers to feel they can stay on in their jobs.
Mrs May faced calls to stand down from members of the public following a chaotic day which saw two leading ministers quit the Cabinet.
One caller to the half-hour grilling on LBC told the PM that Jacob Rees-Mogg would make a better leader, while another said she had "appeased" the EU like Neville Chamberlain in his negotiations with Hitler.
Asked whether she could afford the loss of Mr Gove from her team, Mrs May told LBC: "I want all of my colleagues in the Cabinet to feel able to carry on doing the excellent job they are doing."
She said the Environment Secretary had been doing "a great job", adding: "I haven't appointed a new Brexit Secretary yet, but obviously I will be doing that over the course of the next day or so."