Mr Boles was applauded by some MPs for quitting after his Brexit alternative plan - seen by many as a "soft" Brexit which would have involved continued participation in the single market and a “comprehensive customs arrangement” - was defeated for a second time, with his announcement met with cries of: "Oh Nick, don't go, come on."
Raising a point of order, he told the Commons: "I have given everything to an attempt to find a compromise that can take this country out of the European Union while maintaining our economic strength and our political cohesion.
"I accept I have failed. I have failed chiefly because my party refuses to compromise."
Cabinet will now meet on Tuesday for five hours to thrash out a way forward.
Comments made in the Commons by Brexit Secretary Steve Barclay has raised suspicion thatthe Prime Minister is seeking to bring back her Brexit deal for a fourth time if she believes she has enough support for it.
Mr Barclay told MPs: "This House has continuously rejected leaving without a deal, just as it has rejected not leaving at all.
"Therefore the only option is to find a way through which allows the UK to leave with a deal. The Government continues to believe that the best course to take is to do so as soon as possible."
What are the results from the second round of indicative votes and what does it mean for the Prime Minister?
Speaker John Bercow announced the results as follows for the indicative votes procedure:
Customs Union - defeated by 276 votes to 273, majority three.
The plan would have required any Brexit deal to include, as a minimum, a commitment to negotiate a “permanent and comprehensive UK-wide customs union with the EU”.
Common market 2.0 - defeated by 282 votes to 261, majority 21
The motion proposed UK membership of the European Free Trade Association and European Economic Area.
It would have allowed continued participation in the single market and a “comprehensive customs arrangement” with the EU after Brexit – including a “UK say” on future EU trade deals – would remain in place until the agreement of a wider trade deal which guarantees frictionless movement of goods and an open border in Ireland.
Second referendum - rejected by 292 votes to 280, majority 12.
This motion would have required a public vote to confirm any Brexit deal passed by Parliament before its ratification.
No-deal or revoke - rejected by 292 votes to 191, majority 101
This plan would have sought an extension to the Brexit process, and if this was not possible then Parliament would choose between either no-deal or revoking Article 50.
Discussing the significance of the results ITV News Political Editor Robert Peston said: "The two most important results tonight are that the confirmatory referendum got more votes than any other option and Clarke’s customs union option lost by the narrowest option."
He said Monday night's results suggested two positive outcomes for the Prime Minister.
"On the referendum proposal and on Nick Boles' very soft Brexit proposal, 24 to 25 Labour MPs rebelled against Jeremy Corbyn on both of those," he said.
"Now she [Mrs May] will now be calculating, hoping that she can persuade those Labour MPs to back her deal if she brings it back to the commons."
Eight Brexit options were rejected in the Commons last week as MPs attempted to determine a majority on an alternative Brexit plan.
Peston added that the probability of a no-deal Brexit is now even greater as "neither the Government or Parliament is able to answer the simplest question from the EU's 27 leaders, namely 'what exactly would you do with any delay to Brexit to end all the cancerous uncertainty'".
What is the reaction to the results?
Labour leader Jeremy Corbyn said: "It is disappointing that no solution has won a majority this evening.
"But I remind the House the Prime Minister's unacceptable deal has been overwhelmingly rejected three times."
He suggested the "house should have a chance to consider again the options" put before them on Monday "so the house can succeed where the Prime Minister has failed".
Conservative MP Mark Francois said the results were "an attempted coup against the British people".
In a heated exchange with ITV News Political Correspondent Paul Brand, Mr Francois said MPs were trying to "impose a Customs Union completely against the wishes of 17.4 million people".
Tory MP Nicky Morgan told ITV News the results were "agony" for "everyone watching".
European Parliament Brexit coordinator Guy Verhofstadt said Monday night's events meant a hard Brexit is now "inveitable".
He tweeted: "The House of Commons again votes against all options. A hard Brexit becomes nearly inevitable.
"On Wednesday, the U.K. has a last chance to break the deadlock or face the abyss."
Watching the reaction from Mr Boles, former Tory MP Anna Soubry extended a welcoming hand inviting him to join The Independent Group.
She told ITV News "there would always be a place" for Mr Boles in the newly-formed group.
What happens next?
On April 3 backbench MPs will again take charge of the Commons timetable to consider Brexit plans under Tory MP Sir Oliver Letwin's scheme to break the Parliamentary deadlock.
Wednesday April 10
An emergency summit of European Union leaders will consider any request by the UK for a longer delay to Brexit. To be granted a further postponement the Government will have to set out what purpose it would achieve and it will almost certainly involve taking part in the European elections.
Friday April 12
The UK is scheduled to leave the EU on April 12 after MPs rejected the Prime Minister's deal last week.
Thursday May 23
If Europe's leaders have agreed an extension to the Article 50 process, the UK will elect MEPs to the European Parliament.