Speaking at a late night press conference in Strasbourg following talks with EU Commission president Jean-Claude Juncker, May said: "The deal that MPs voted on in January was not strong enough in making that clear - and legally binding changes were needed to set that right".
Prime Minister Theresa May rushed to Strasbourg on Monday evening to seek concessions from the European Union in a last-ditch attempt to avoid another humiliating defeat in Parliament of her deal to exit the bloc.
Commenting on the Strasbourg agreements, the Attorney General wrote: "I now consider that the legally binding provisions of the Joint Instrument and the content of the Unilateral Declaration reduce the risk that the United Kingdom could be indefinitely and involuntarily detained within the Protocol's provisions at least in so far as that situation had been brought about by the bad faith or want of best endeavours of the EU".
She claims the changes now means the Irish backstop - the insurance policy created to avoid a hard border in Ireland - could not "become permanent".
Nick Boles, a leading Conservative pushing the government to rule out a no-deal Brexit, warned May that she would "forfeit the confidence of the House of Commons" if she failed to put it to a vote.
Shadow Brexit secretary Sir Keir Starmer said Cox had confirmed that "no significant changes" had been secured to the Withdrawal Agreement and the government's strategy was "in tatters".
"If MPs vote for Theresa May's Brexit deal, we edge closer to understanding exactly how and when Brexit will play out but whether that is positive or negative for the pound depends on the deal itself".
"Now is the time to come together to back this improved Brexit deal and deliver on the instruction of the British people". However, the text of the 585-page withdrawal agreement remained unchanged.
US Grounds All Boeing 737 Max Planes
Federation Aviation Administration has affirmed the planes' airworthiness and that investigations were ongoing. We remain confident in the safety and airworthiness of the MAX 8 .
Cox gave his legal opinion on the new wording struck between May and Juncker - which could be crucial in determining how Brexiteers vote later Tuesday.
Ranko Berich, head of market analysis at Monex Europe, said: "we are now back to a base case where May's deal is rebuffed and she is forced to seek an extension".
Today (12 March), UK parliament will vote on whether to accept May's Brexit deal or not.
If they vote yes to extend Article 50 then the United Kingdom will ask for a short extension.
On the other hand, the opposition Labour party, with its 247 MPs, is likely to reject May's proposal.
Mrs May promised lawmakers a vote on her deal this Tuesday. It they vote yes then Brexit would take place with May's deal on or around 29 March.
May might even try a third time to get parliamentary support in the hope that hardline eurosceptic MPs in her Conservative Party, the most vocal critics of her withdrawal treaty, might change their minds if it becomes more likely that Britain might stay in the European Union after all.
Labour Party leader Jeremy Corbyn urged MPs to vote against the deal when it returns to the Commons, saying May had "recklessly run down the clock" on negotiations.