In an interview with The New York Review of Books Mr Barnier warned the deal already offered to the UK government by the EU is the only deal available.
Mr Barnier said: “There are three options: a deal based on the agreement finalised six months ago; withdrawal without a deal; or no Brexit.
“It will have to be the choice of the UK. During the last three years, we have delivered what the UK wants: leaving the EU, leaving the single market, leaving the customs union [after the Irish “backstop” is resolved].
“Even if we regret their decision profoundly, it is their sovereign decision and we have to respect it.”
The pointed message can be read as a warning to leadership hopefuls who have promised to renegotiate the Brexit deal.
MPs, Jeremy Hunt, Dominic Raab, Matt Hancock and Mr Johnson have all said they would renegotiate the backstop if they were to replace Mrs May.
Mr Raab said he would tear up the backstop and pursue plans to put alternative arrangements in place to avoid a hard border.
Mr Hunt has also said he wants to replace the Northern Irish backstop with “alternative arrangements”.
Mr Barnier also said some people voted for Brexit in the UK as they did not want to accept the EU’s rules.
He said: “There were, also, people voting for Brexit who simply don’t want to accept rules.
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“Some based in the City of London voted to leave, as they don’t want to accept the Union’s regulations on their trading; they want to speculate freely and the Union doesn’t allow them to do so.”
Mr Barnier said he wants the UK to remain a partner, friend and ally of the EU and so the relationship between the two parties must be “constructive”.