"We have had a very constructive meeting of our assembly group and I had the opportunity to put to them proposals which we have been working on," said Mr Robinson.
"Everyone present believes that this is consistent with our election manifesto and pledges we have made to the people.
"We look forward to going to Hillsborough and the document should be published."
The deal is believed to include new arrangements on the oversight of loyalist parades.
DUP assembly member Nelson McCausland said the loyalist marching groups would be very satisfied by what had been agreed and it should eventually lead to new legislation on parades.
Mark Devenport, BBC NI political editor
The five sections of the deal
The first on policing and justice will set a date of 12 April as date for the devolution of policing and justice powers. It will also deal with the operational independence of the chief constable.
Secondly, a working group to look at reforming the regulation of parades will be set up. That group will report back within a month with a view to getting legislation to the Assembly by June.
Thirdly, there will be details laying out the relationship between the Justice Minister and the rest of the Executive.
Fourthly, there will be a commitment to tackle the "dysfunctionality" of the Executive. The two ministers from smaller coalition parties, the SDLP and UUP, will take the lead in this.
Fifthly, there will a move to free legislation which has become "trapped" in the system.
He said there was no mention of either a new policing college or the savers of the Presbyterian Mutual Society in the document.
Sinn Fein leader Gerry Adams welcomed the DUP's decision and said: "There's a wonderful chance now in a new spirit for us all to go forward.
"This isn't just about structures or protocols, it obviously has to be about inspired leadership and people accepting in leadership positions that the citizens want this to work."
He said there had not been enough movement on the Irish language but that was "work for another day".
Commending his own party's negotiating team, he added: "I believe that the Assembly and political institutions can now proceed on the basis of equality, fairness and partnership.
"They also have to deliver for all citizens, that is the collective responsibility of all the political parties."
On Thursday night Mr Robinson said there was a basis for a deal which he could recommend to his party and to the community.
DUP assembly members gathered at Stormont at about 2200 GMT.
"An essential element of the Democratic Unionist manifesto is the requirement for community confidence and we believe that this can be the basis of gaining that confidence," Mr Robinson said.
"It does more than dealing with devolving further powers. It deals with how we deal with the powers that we have."
The DUP decision has been welcomed by Alliance Party leader David Ford, who is widely tipped to be the new justice minister.
He said: "This is what the people of Northern Ireland have waited so long to hear and it means that the Executive can get back to the real work of providing quality services and strengthening our economy.
"We may face a few challenges in the coming months as regards the justice devolution process, but I am very hopeful that this will signal a new, more positive era for Northern Ireland."
SDLP leader Mark Durkan said he always thought a deal would be "scrambled over the line".
"What we need to see now when we see the deal this morning is does it answer all of the questions and all of the issues," he said.
"We will have to take our turn with other parties in proofing what is proposed, not trying to create problems, but pre-empting any possible shortcomings or problems there are with it so we can actually improve it."
However, Traditional Unionist Voice, which opposes mandatory coalition with Sinn Fein, described the DUP as "snowmen who had melted".
Its leader Jim Allister said: "The DUP MLAs who buckled tonight not only let themselves down, but, more importantly, let their country down."
Referring to the fact that 14 DUP assembly members reportedly voted against a deal on the table on Monday, he added: "The deal the DUP so meekly accepted tonight is the same deal they rejected.
"The deal hasn't changed, only the snowmen of the DUP who melted once the heat came on."
Earlier on Thursday it emerged that policing and justice powers could be transferred to Northern Ireland in April if the DUP and Sinn Fein were able to reach a deal.
Talks between the British and Irish governments, Sinn Fein and the DUP have been going on for the last 10 days.
The relationship between Sinn Fein and the DUP - Northern Ireland's two biggest political parties - has been strained for some time because they disagreed about the timetable for the transfer of policing and justice powers from Westminster to Stormont.
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