"It is with regret that I hereby tender my resignation as a Minister in the Government Whips' Office", Johnson wrote in a letter to May, published on his Facebook page. "This agreement prevents us from taking back control and instead could leave us perpetually constrained by the European Union".
He cited "personal objections" to the Brexit plan in general, and the backstop solution for the Irish border in particular.
The politician has served as Parliamentary Private Secretary to the Secretary of State for Exiting the European Union since June 2017.
The UK has planned to leave the bloc by 29 March; however, earlier in the day, President of the European Council Donald Tusk and President of the European Commission Jean-Claude Juncker hinted that Brussels was ready to extend the transition period for London.