DUP Leader Arlene Foster says she has discussed the confidence and supply agreement with new Conservative Party Leader Boris Johnson.
Mr Johnson defeated rival Jeremy Hunt in a poll of Tory members by 92,153 votes to 46,656.
He will be installed as Prime Minister by the Queen on Wednesday, after Theresa May formally resigns from office.
Mr Johnson faces a daunting in-tray at Number 10, including keeping his "do or die" promise to meet the looming Brexit deadline of 31 October.
But one of his first tasks will be to lock down the confidence and supply arrangement with the DUP, which keeps the Conservative Party in power.
Arlene Foster said she has now spoken with Mr Johnson - and said the agreement remains in place and will be reviewed in the coming weeks.
“I have spoken with Boris Johnson and congratulated him on becoming leader of the Conservative Party," she said.
"We discussed our shared objectives of strengthening every part of the union, ensuring the 2016 referendum result is implemented and seeing devolution restored in Northern Ireland.
"That agreement included a review between each Parliamentary session.
"This will take place over the coming weeks and will explore the policy priorities of both parties for the next Parliamentary session.
"I also look forward to welcoming Mr Johnson back to Northern Ireland shortly after becomes Prime Minister.”
Earlier, the DUP Deputy Leader Nigel Dodds told UTV he is "very confident we’ll be able to work closely together in the coming months".
Meanwhile, Sinn Féin Stormont leader Michelle O'Neill said: "Boris Johnson, the Tory party in general, are at the heart of our problems here on the island of Ireland.
"They're actually at the heart of the fact we've had an impasse here for over two and a half years where this Assembly and this Executive hasn't sat.
"At the heart of that is the fact that the reckless Brexit agenda, at the heart of those problems is also the fact that they have a cosy relationship - which is toxic to our politics here - with the DUP.
"So I think Boris Johnson won't be any addition in terms of the politics, he hasn't played a very positive role in the last number of years."
Northern Ireland's other parties have also been reacting to the news.
SDLP Leader Colum Eastwood said Mr Johnson’s election is “a worrying step toward a hard no-deal Brexit and a hard border in Ireland”.
He went on: “Johnson has coasted into Downing street on a wave of Brexit bluff and bluster.
“It won't be long until he crashes into the rocky reality that the European Union will not sacrifice the interests of Ireland to appease a man who has lied and slandered its institutions in an effort to secure power.”
UUP Leader Robin Swann congratulated Mr Johnson.
He added: “The bottom line for the Prime Minister is that any decisions he takes must be in the best interests of all of the United Kingdom and that includes doing everything possible to avoid a no-deal Brexit.
“I urge him not to allow nationalism in Northern Ireland or Scotland to exploit the current instability for selfish political interests.
“I look forward to meeting Boris Johnson soon to make those points directly.”
Alliance Party Leader Naomi Long said the UK "needs a statesman, not a showman".
She added: “To date he has failed to demonstrate any real understanding of the needs of Northern Ireland, particularly in the context of Brexit and especially in a no deal scenario - needs that require more than merely a ‘can do’ attitude to resolve."
Green Party NI Leader Claire Bailey said: "The reality is that Boris Johnson has no chance of commanding a majority in a Brexit-ravaged Westminster.”
The Northern Ireland Conservatives said: "It is with great excitement that we look forward to supporting his vision of change, which has inspired members from Belfast to London."