Some 55 per cent of the public think the planned deal, on which parliament will also get to vote, will be good for Britain, rising to 81 per cent among Leave voters and versus 19 per cent who believe it is bad.
Among Remain voters, almost a third believe it will be good for Britain, though May has failed to swing the majority of them around to her way of thinking – 38 per cent believe it will be bad for the country.
Read more: May's plan for Brexit is bold and ambitious
The majority of those polled after the Prime Minister's speech – 53 per cent – also said they would be personally happy if Britian managed to achieve the deal, which would see the country leave the Single Market but negotiate new agreements with the 27 member states.
The PM appears to have fulfilled her promise to abide by voters' decision to leave Europe, with the majority saying the deal respects the outcome of the referendum, irrespective of which way they voted, even among Remain voters. Among Leave voters, this has been found to be their top priority in negotiations.
In terms of May's ability to negotiate the kind of deal she laid out, more people are confident she can achieve it than not – 47 per cent versus 38 per cent.
But, May's attempts to play hardball with a "no deal is better than a bad deal" threat (which just under half of Brits agree with), is not necessarily seen as a tactic that will achieve the desired results. Most people believe its unlikely the EU will agree to the deal (56 per cent), even among Leave voters.
And ultimately, 46 per cent still stand behind the decision to leave Europe, compared to 42 per cent looking back in hindsight who think it was wrong to vote to leave.
YouGov's Anthony Wells said:
Our initial polling, conducted on Tuesday night and Wednesday, suggests the announcement went down well. All of the key negotiating points we asked about met with majority support.
Most were uncontroversial and supported by both Remain and Leave voters: control of immigration, an open border with Ireland, guaranteeing the rights of existing EU immigrants and continuing to work with the EU on security matters all received over 70 per cent support.
However, there was some disagreement between Remain and Leave Voters on the matter of the Single Market and customs union. Wells said that "people won't judge Brexit on the minutiae of the deal" but "on the overall package, on whether it feels like a good deal for Britain or not."
"By that measure, Theresa May's announcement was a success," he said.
"Theresa May has passed her first Brexit test: she has managed to define a form of Brexit that the majority of the country can get behind. Getting the rest of Europe to agree to those proposals may be a more difficult challenge."