The memo demands the Prime Minister, who looks increasingly fragile following the departure of two of her Cabinet ministers in as many weeks, "underline her resolve" for leaving the European Union, according to The Mail on Sunday.
The letter also sets out a date for transition arrangements between the EU and UK to end of 30 June 2021, the newspaper said.
Mr Johnson and Mr Gove are also said to have urged the Prime Minister to ensure members of her top team fall behind their Brexit plans by "clarifying their minds" and called for them to "internalise the logic".
The leaked letter appears to make a thinly veiled attack on Chancellor Philip Hammond, who backed remain and wants a softer Brexit, for lacking the "sufficient energy" in preparing to the UK's future outside the bloc.
A senior Government source told the Mail the Foreign Secretary and Environment Secretary had conducted a "soft coup" and described Ms May as "their Downing Street hostage".
The letter, titled EU Exit - Next Steps, is marked "For your and Gavin's eyes only", a reference to the PM's chief of staff Gavin Barwell.
It states: "Your approach is governed by sensible pragmatism. That does not in any way dilute our ambition to be a fully independent self-governing country by the time of the next election.
"If we are to counter those who wish to frustrate that end, there are ways of underlining your resolve.
"We are profoundly worried that in some parts of Government the current preparations are not proceeding with anything like sufficient energy.
"We have heard it argued by some that we cannot start preparations on the basis of 'No Deal' because that would undermine our obligation of 'sincere co-operation' with the EU. If taken seriously, that would leave us over a barrel in 2021.
"We all want you to push your agenda forward with confidence and have your Government articulate the following..."
The letter suggests both men have set aside their differences following last year's Tory leadership contest, when Mr Johnson dramatically ruled himself out of the race after Michael Gove’s shock entry into the contest.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies