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 three criticised the government’s “disastrous handling” of Brexit and said it had undone “all the efforts to modernise” the Conservatives.
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 – saying it represented “the centre ground of British politics”.
At a press conference on Wednesday, Ms Soubry said of the Conservative party: “The battle is over, the other side has won.
“The right wing, the hard-line anti-EU awkward squad that have destroyed every leader for the last 40 years are now running the Conservative Party from top to toe. They are the Conservative Party.”
The departure of the three MPs has reduced the government’s working majority to nine MPs, and Ms Allen claimed there were “absolutely” other colleagues “keen” to join the group.
The Independent Group now has more MPs in Parliament than the Democratic Unionist Party and equals the number of Liberal Democrats.
A tweet from the Independent Group welcomed the new members, adding: “Both our parties are broken. We are going to #ChangePolitics for the better.”
A Labour spokesman criticised the group, saying they had formed “what is effectively an establishment coalition based on the failed and rejected policies of the past”, such as austerity, corporate tax cuts and privatisation.
Minor tremor or political earthquake?
By Iain Watson, BBC political correspondent
Perhaps the way the new Independent Group might change the political dynamic is this: Their mere existence tells the leadership of the traditional parties that if they don’t listen to the concerns of their parliamentarians they, and some of their voters, really do have somewhere else to go.
So they present a challenge to those at the top of the existing parties.
How – and if – the leaderships of these parties change could determine whether the defections eventually register on the political Richter scale.
In the letter, the former Tory MPs – who all support the People’s Vote campaign for another EU referendum – said the party was “in the grip” of the DUP and the pro-Leave European Research Group over Brexit, and said there had been a “dismal failure” to stand up to them.
They wrote: “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.”
The three MPs said they will support the government on areas such as the economy, security and improvements to public services, but they felt “honour bound to put our constituents’ and country’s interests first” over Brexit.
They told Mrs May in their letter: “We voted for you as leader because we believed you were committed to a moderate, open-hearted Conservative Party.
“Sadly, the Conservative Party has increasingly abandoned these principles and values with a shift to the right of British politics.”
Image captionHeidi Allen (fourth from left), Anna Soubry and Sarah Wollaston appear in Parliament with the Independent Group
In an email to her constituents, Ms Soubry said she now had more in common with her fellow Nottinghamshire MP Chris Leslie – a founding member of the Independent Group and former Labour member – than many in her own party.
“It is time to realign British politics and get back to the centre moderate ground,” she said.
And Ms Allen highlighted her concerns around poverty, as well as Brexit, in a statement, saying: “I can no longer represent a government and a party who can’t open its eyes to the suffering endured by the most vulnerable in society – suffering which we have deepened whilst having the power to fix.”
Ms Allen said she was “excited” about the future, adding: “I want to be part of something better, a party that people vote for because they want to, not because they feel they have to.”
Liberal Democrat leader Sir Vince Cable said his party would “hold out the hand of friendship” to the Independent Group and said they already had “a good working relationship” with the MPs.
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.”
The party’s deputy chairman, Tory MP James Cleverly, told BBC Radio 5 Live that the resignations were “very sad and disappointing”, which was echoed by Communities Secretary James Brokenshire. But he added that the focus “has to remain on delivering Brexit” and the Conservative party was “a broad church and will remain so”.
Work and Pensions Secretary Amber Rudd said it was a “great shame to have lost the commitment and undeniable talent” of the three MPs.
Remain-backing Tory MP Nicky Morgan said the party “should regret losing three such talented women from the Conservative Party”.
Former Cabinet office minister, Damian Green, tweeted that he hoped the three MPs rejoined the party one day.
Some Labour MPs have been criticising their former colleagues for joining forces with ex-Conservatives.
Shadow education secretary Angela Rayner said it was “a new low” to see the MP of her home town, Ann Coffey, welcoming an MP responsible for government cuts, adding: “I’m utterly disgusted.”
Scottish Labour MP Danielle Rowley also questioned her former colleagues, tweeting: “How people who once called themselves Labour can cosy up next to the likes of Soubry, smiling and laughing, is absolutely beyond me.
“I guess we now know how their policies and values differ from Labour.”
Others have been criticising the group for not holding by-elections to win back their seats as independent MPs.
Douglas Carswell, who resigned from the Conservatives to join UKIP in 2014, tweeted: “When I changed parties it didn’t occur to me to not hold a by election. If my own electorate weren’t supportive, what was the point?”
However, Ms Allen rejected calls for them to step down to contest by-elections, saying: “This is what the big parties do. They want to crush the birth of democracy. They want to crush people like us trying to change things for this country.
“This is the game, of course, they will play but we are better than that, and we think our constituents and the country deserve better than that.”
