Finance Minister Simon Hamilton said the deal agreed on Thursday afternoon includes a 2.1% cut to all Stormont departments except health and education.
He said this will mean a £78m reduction to the departmental resource budgets, with justice (DOJ), social development (DSD) and employment and learning (DEL) taking the biggest hits.
A statement from the DUP minister went on: "Given the significant pressures facing the Executive's budget this year, it has been necessary to agree an immediate 2.1% reduction to departmental resource budgets in order to provide funding for a range of Executive commitments."
Mr Hamilton said these include the Historical Institutional Abuse Inquiry and local government reform and a "much needed allocation" of £20m to the Department of Health.
Agreement was delayed by four weeks after the DUP and Sinn Féin clashed over how to deal with the Treasury's demand for £87m in financial penalties, caused by a failure to agree welfare reforms.
The DUP wanted money to be set aside but Sinn Féin said no.
Mr Hamilton said the Executive has agreed that the reductions should occur in the October monitoring round but will "undoubtedly have a detrimental impact on our public services".
He continued: "Further reductions to departmental budgets amounting to £87m will be required as a consequence of welfare reform not progressing. Those failing to proceed with welfare reform bear sole responsibility for the dire consequences that will follow."
The agreement on the June Monitoring Round was reached despite Alliance ministers voting against it and the Ulster Unionist Party abstaining.
Regional Development Minister Danny Kennedy of the UUP said the two main parties - the DUP and especially Sinn Féin - are guilty of "voodoo economics".
His party added: "We are also totally disgusted that the Executive is not going to fully fund the concessionary fares scheme - one of their own priorities. This scheme is something the Ulster Unionist Party is passionate about and Danny Kennedy will fight to protect it."
Justice Minister David Ford, of the Alliance Party, has accused Sinn Féin and the DUP of grossly mismanaging public finances.
He continued: "It's politically clever in the short term, but financially stupid in the long term.
"They have torn up the rule book for properly managing public finances. People need to know that today's political deal doesn't mean that the budget crisis has been resolved - it's made it worse."
It’s a fix on the basis of one for the DUP and one for Sinn Féin
Even with agreement being found in the June round, the seeds of disagreement over the next round - which will consider the £87m penalties - were already apparent.
Sinn Féin doesn't accept the penalties will have to be taken out while the DUP insist they will.
Education Minister John O'Dowd, SF, said: "What we have accepted here is the June monitoring paper, it is outlined there - the proposals are there for everyone to see.
"We will now move into discussion and negotiation on the October monitoring round.
"That is several weeks away and there are a number of unknowns including a statement from the British government in relation to their budget priorities so all of those things will need to be taken into account before we can determine what will or will not be in the October monitoring round."
However the First Minister, DUP leader Peter Robinson, said: "John O'Dowd clearly doesn't understand what the document said.
"The document said that £13m has already been taken from the budget so the penalties are already underway and a further £87m has to be taken into account in October."
SDLP deputy leader Dolores Kelly said the "cobbled together deal" is "already falling apart".
She continued: "This another example of bad government from the DUP and Sinn Féin who are responsible for some very poor decision making.
"We will be facing another monitoring round in a couple of months. It seems evident that some form of Executive summit to manage the rest of the financial year is now required."
Meanwhile a health department spokesman said minister Edwin Poots of the DUP has welcomed the announcement of the extra £20m, despite earlier calls for £160m.
A statement continued: "While, the allocation will go some way to addressing a range of pressures in front line services such as emergency care, very significant financial challenges still remain.
"The Minister has highlighted to the Executive the implications of this increasingly challenging financial scenario. Looking forward, he now faces difficult decisions and he will give these his full consideration in order to minimise any detrimental impacts on Health and Social Care services."