The announcement that Brexit talks are set to move on to issues of trade and transition was welcomed by UK business leaders.
But opposition politicians questioned whether the deal struck between the UK and the European Commission would satisfy hardline Brexiteers on the Conservative benches.
Breaking: Brexit talks 'breakthrough' for Theresa May in EU negotiations
Stephen Martin, director general of the Institute of Directors, said: "It went right down to the wire, but businesses will be breathing a huge sigh of relief."
He added: "The most pressing concern for UK companies has been their EU staff, who have urgently needed certainty about their future in this country.
"We have grounds to hope now that our members will be able to send their employees off for the Christmas break feeling more comfortable about their status here.
"We call on the UK and EU to build on this positive momentum going into the New Year.
"It is overwhelmingly in the interests of both sides to begin working on our future economic relationship - particularly in order to fully address the Irish question.
"And we look forward to further clarity about what the UK's objectives are for that new relationship as well as a firm commitment on transition in the very near future."
A spokesman for the Liberal Democrats, who are fighting for UK voters to be given a second referendum on any final Brexit deal, said: "So Theresa May has finally got a deal, but how long before it's torn apart by her own MPs?
"It should be the British people, not Tory Brexiters and DUP, who get to decide whether this deal is good enough."
The Lib Dem spokesman said there was "still no solution over how to prevent a hard border between Northern Ireland and Ireland" in the text of the joint report.
"A huge obstacle to the Government's Brexit plans is being kicked into the long grass," he said.