Anna Soubry, Sarah Wollaston and Heidi Allen wrote a joint letter to Theresa May to confirm their departure.
The PM said she was “saddened”, but her party would “always offer… decent, moderate and patriotic politics”.
The pro-Remain trio will join the new Independent Group – made up of eight Labour MPs who resigned from their party over its handling of Brexit and anti-Semitism.
In the letter, they said the party was “in the grip” of the Democratic Unionist Party and the European Research Group over Brexit, and said there had been a “dismal failure” to stand up to them.
And they claimed leaving the EU had “redefined the Conservative Party – undoing all the efforts to modernise it”.
They added: “We find it unconscionable that a party, once trusted on the economy, more than any other, is now recklessly marching the country to the cliff edge of no deal.”
Theresa May said the UK’s membership of the EU had been “a source of disagreement both in our party and our country for a long time”, so “ending that membership after four decades was never going to be easy”.
But, she added: “By delivering on our manifesto commitment and implementing the decision of the British people we are doing the right thing for our country. And in doing so, we can move forward together towards a brighter future.”