Party leader Peter Robinson said just before 0000 GMT that the decision to back the deal had been "unanimous" among the party's 35 assembly members.
Sinn Fein president Gerry Adams has welcomed the DUP's decision.
It is understood the British and Irish prime ministers will travel to Northern Ireland on Friday morning.
"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 tomorrow to Hillsborough and the document should be published."
Mr Adams said the DUP's decision had followed "a lengthy stretch of negotiations".
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."
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.
FINALLY. I swear NI politicans are the biggest load of posturing old fannys. And seeing the docu-drama Mo on Channel 4 last Sunday just makes me miss her all the more because she just didn't take any of their crap.