Responding to the government's defeat, Leader of the House, Andrea Leadsom, told MPs that the final and full legal advice would be published on Wednesday.
The outcome forced May's team to promise to release the full tome ahead of next Tuesday's vote on the contentious Brexit agreement.
Critics of the government said they suspect the advice will reveal the Attorney General Geoffrey Cox's misgivings about the Brexit agreement.
MPs debated long into the night in the first of five sessions set aside for the Brexit deal, culminating with a vote on Tuesday December 11.
Mr Grieve said: "Parliament has tonight asserted its sovereignty to ensure that amendments - such as for a People's Vote - can be made to any motion if or when the Government's proposed deal for leaving the European Union has been defeated". "By treating Parliament with contempt, the Government has proved it has lost its majority and the respect of the House".
Soft-liners are against the deal because they believe that it won't secure the closest possible British-EU political and economic ties.
British Prime Minister Theresa May brushed aside questions Monday about whether she will resign if her Brexit deal is rejected by Parliament next week, saying she's confident she'll still have a job after the crucial vote.
Opposition parties say their representatives will vote against the deal, and so have dozens of lawmakers from May's Conservative Party.
"We have listened carefully and in light of the expressed will of the House, we will publish the final and full advice provided by the attorney general to cabinet", Leadsom told parliament.
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Rising interest rates in advanced economies and trade tensions have increased pressures on emerging markets recently. The Group of 20 brings together leaders of 19 of the world's most industrialised nations plus the EU.
She said the Government, which had sought to slow down the process by referring the issue to Parliament's Committee of Privileges, had fulfilled the spirit of the order to publish.
Tory MPs Peter Bone and Philip Hollobone backed the contempt motion, along with nine MPs from the DUP - who are supposed to be Mrs May's parliamentary allies.
"The Government must not be allowed to use this chaotic situation to take focus away from the mess they are making of Brexit".
Mrs May said Britain will leave regardless of any future decision by the EU's top court and that the choice is between her deal or no deal.
Defeat would leave the United Kingdom facing a chaotic "no-deal" Brexit and could topple the prime minister, her government, or both.
If her deal falls in the "meaningful vote" next week, the PM has 21 calendar days to set out a statement on her next steps.
Bank of England Governor Mark Carney denied accusations of scaremongering after the bank said last week that, under a worst-case Brexit, Britain could suffer greater damage to its economy than during the financial crisis of 2008.
Advocate General Campos Sanchez-Bordona said he believed Britain could revoke Article 50 without agreement from other European Union states.
"This is a huge win for us, and a huge step forward from the highest court in the business, and confirms what we have been hoping for: that the United Kingdom can indeed change its mind on Brexit and revoke Article 50, unilaterally", he said.
"I never said this deal was ideal, it was never going to be".