The junior minister at the Department of Environment, Food and Rural Affairs (Defra) said in his resignation letter to the Prime Minister that he wanted to be “free to participate in the critical debate that will take place in the weeks ahead”.
Mr Eustice accused MPs seeking a delay to the UK’s exit of having “terribly undermined” the Prime Minister, and hit out at the EU for not having “behaved honourably” in negotiations.
Mrs May caved in to pressure from pro-EU ministers to allow a vote on extending Article 50 and delaying Brexit if her deal is rejected by MPs a second time.
But Brexiteers in her own party mounted a show of strength in votes on Wednesday night, with over 100 Tory MPs breaking a three-line whip to oppose the move.
Mr Eustice, who was minister for agriculture, fisheries and food, wrote: “It is with tremendous sadness that I have decided to resign from the government following the decision this week to allow the postponement of our exit from the EU.”
His letter went on: “I have stuck with the government through a series of rather undignified retreats.
“However, I fear that developments this week will lead to a sequence of events culminating in the EU dictating the terms of any extension requested and the final humiliation of our country.
“I appreciate that you have been terribly undermined by those in Parliament who refuse to respect the referendum result. You have shown tenacity and resilience over the past year.
“However, what our country needs from all its political leaders at this critical juncture is courage, and we are about to find out whether Parliament has it.”
Mr Eustice adds: “If the position of Parliament is now that we will refuse to leave without an agreement then we are somewhat stuck.
“This is uncomfortable for everyone, but we cannot negotiate a successful Brexit unless we are prepared to walk through the door. We must therefore have the courage, if necessary, to reclaim our freedom first and talk afterwards.”
In her reply, the Prime Minister insisted her “absolute focus” was on “getting a deal that can command support in parliament and leaving on 29 March”.
As a leading campaigner for a Leave vote in the EU referendum, Mr Eustice promised Scottish fishermen that powers over the sector would “automatically” pass to the Scottish Parliament.
The issue has since become mired in a “power grab” row between Edinburgh and London, and vital legislation on agriculture and fisheries has not been passed.
SNP Westminster leader Ian Blackford said Mr Eustice’s resignation was “beyond parody”.
“This is not a functioning government, it is the Tory party at war with itself under a Prime Minister who can’t give leadership,” Mr Blackford said.
Liberal Democrat MP Tim Farron said: “It is odd that the minster has resigned complaining about Brexit delays when his department has delayed new laws on agriculture and fisheries post-Brexit.”