Davis, who was appointed to the post in 2016 and was responsible for negotiating the UK's EU withdrawal, told May in a letter that the government's proposal "will leave us in at best a weak negotiating position, and possibly an inescapable one"
In a major blow to Prime Minister Theresa May, Britain's Brexit Secretary David Davis has resigned from the government citing irreconcilable differences with the premier over her plan to make a soft exit from the EU.
Davis quit just two days after May secured Cabinet backing for her strategy for a divorce deal with the EU.
Davis, who was appointed to the post in 2016 and was responsible for negotiating the UK's EU withdrawal, told May in a letter that the government's proposal "will leave us in at best a weak negotiating position, and possibly an inescapable one."
In his resignation letter, Davis told May "the current trend of policy and tactics" was making it "look less and less likely" that the UK would leave the customs union and single market.
He said he was "unpersuaded" that the government's negotiating approach "will not just lead to further demands for concessions" from Brussels.
In her reply, May said: "I do not agree with your characterisation of the policy we agreed at Cabinet on Friday."
She said she was "sorry" he was leaving but would "like to thank you warmly for everything you have done... to shape our departure from the EU".
His resignation undermined May's already weak government, which has lost several ministers in the past year over sexual misconduct allegations and other scandals.
His resignation comes as May is due to brief lawmakers on her EU exit plan.
The departure of a key minister could lead to further departures and throw May's government into chaos just as it enters a key period of negotiations with the EU.
According to reports, Davis' deputy, Steve Baker, and another Brexit sitminister, Suella Braverman, may also be on their way out.
The June 2016 vote to leave the European Union effectively ended a relationship which had endured for 44 years. Article 50 of the Lisbon Treaty outlines the voluntary departure, which will take effect in March 2019.
Failure to agree conditions with the EU before March would result in a "no-deal" Brexit that could wreak havoc on the UK's relationship with its biggest export market, leaving it with no arrangements on staying in or having access to the customs union and single market.
Opposition leader Jeremy Corbyn said that Davis' resignation "at such a crucial time" shows that May "has no authority left and is incapable of delivering Brexit."