Phillip Lee, a parliamentary under-secretary of state in the Ministry of Justice, revealed his announcement in a speech to a Conservative think tank on Tuesday morning, hours before MPs begin two days of debate on the EU Withdrawal Bill.
Mr Lee, who was previously reprimanded by party whips over his criticism of the government's approach to Brexit, called on fellow MPs and ministers to speak up in favour of an amendment to the crucial Brexit legislation giving the Commons greater control over the final deal with Brussels.
Mr Lee told journalists: "This is not about Remain or Leave. It is because I fear we are having the worst of all worlds forced upon us with a fudge in the middle.”
He tweeted that he was "incredibly sad" to have to resign "so that I can better speak up for my constituents and country over how Brexit is currently being delivered".
The MP for Bracknell also indicated he was in favour of a referendum on the final Brexit deal, adding: "When the Government is able to set out an achievable, clearly defined path – one that has been properly considered, whose implications have been foreseen, and that is rooted in reality not dogma – it should go to the people, once again, to seek their confirmation."
In January, Mr Lee was spoken to by government whips after questioning whether the government could press ahead with Brexit following the publication of internal analysis showing every available model for leaving the EU would harm the economy.
"The next phase of Brexit has to be all about the evidence. We can’t just dismiss this and move on. If there is evidence to the contrary, we need to see and consider that too," he tweeted.
"But if these figures turn out to be anywhere near right, there would be a serious question over whether a government could legitimately lead a country along a path that the evidence and rational consideration indicate would be damaging," he added.
"It’s time for evidence, not dogma, to show the way. We must act for our country’s best interests, not ideology and populism, or history will judge us harshly."