By Rebecca Black and Catherine Wylie, PA
The DUP has welcomed the victory of "committed Unionist" Boris Johnson in the race to become the next prime minister.
The party also confirmed that its confidence and supply deal with the Conservative Party will continue under the new leader.
However, other political parties in Northern Ireland expressed concern at Mr Johnson's election, particularly in terms of the potential implications for Brexit.
Arlene Foster's party has been involved in a confidence and supply deal with the Conservative Party since the 2017 general election.
Mrs Foster said on Tuesday afternoon that she had spoken to Mr Johnson and confirmed that the deal between the two parties would continue.
"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," she said.
"The Confidence & Supply Agreement between the Conservative Party and the Democratic Unionist Party remains. 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 (he) becomes Prime Minister."
Mr Dodds told PA it was a "totally emphatic victory" for Mr Johnson.
"I think it gives Boris a very, very strong hand within his own party to say to those naysayers and people who may be out to thwart the referendum result that really they've got to get this done now and move on and govern in the interest of all of the people of the country," he said.
Asked what he thinks the people of Northern Ireland will make of Mr Johnson becoming Tory leader, Mr Dodds said: "I think that what we want to achieve with Boris is a three-fold set of aims, which is first of all to secure and advance the union of Great Britain and Northern Ireland.
"Boris is a committed Unionist and we will work with him to achieve that objective.
"They also I think want to get Brexit done and dusted. People are fed up with this continued limbo. It needs to be delivered. Whatever people voted in the referendum, the referendum result was a UK-wide one and it needs to be respected.
"And we want to get a deal. Our objective is not a no deal. We understand the need to keep a no deal on the table. We want to get a deal.
"And the third priority for us is to get devolved government back up and running in Stormont and we will be talking to Boris and whoever is the Secretary of State after tomorrow about that as an urgent priority."
Northern Ireland is likely to be high on Mr Johnson's agenda when he becomes prime minister, with his government's reliance on the DUP's 10 MPs to give it a working majority in the House of Commons.
The ongoing impasse over Brexit and the implications for the Irish border, as well as the two-and-a-half-year-old collapse of powersharing government at Stormont, will also ensure the region features prominently in his Downing Street in tray.
Mrs Foster tweeted a photograph of her watching the announcement live at her constituency office in Enniskillen, Co Fermanagh, describing it as a "historic day".
Sinn Fein deputy leader Michelle O'Neill said her party will work to protect the peace process and Good Friday Agreement in all its parts, including the commitment to calling a referendum on Irish Unity.
"The British government has responsibilities and commitments under the terms of the Good Friday Agreement and we will hold them to account.
"We will continue to stand up for Irish interests, for the majority of citizens in the north who voted on a cross-community basis to remain within the EU.
"We will continue to work with the Dublin government and the EU27 to protect Ireland from the catastrophic impact of the reckless Brexit being pursued by Boris Johnson and the hard Brexiteers."
Ulster Unionist Party leader Robin Swann also congratulated Mr Johnson, but warned the job of prime minister comes with "enormous responsibilities", at what he described as "such a critical time in the history of the United Kingdom".
"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," he said.
The SDLP and Alliance Party expressed concern at Mr Johnson's appointment.
SDLP leader Colum Eastwood described it as a "worrying step toward a hard no-deal Brexit and a hard border in Ireland".
"Johnson has coasted into Downing Street on a wave of Brexit bluff and bluster," Mr Eastwood said.
"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.
"All parties in the North must now set our combined efforts to resisting the impulse of this administration to drive off the Brexit cliff edge."
Alliance leader Naomi Long said the UK needs a "statesman, not a showman".
"Everyone will have their own opinion on Boris Johnson and his career to date," she said.
"However, it is now vital as he takes up the reins as prime minister, he demonstrates a level of leadership and seriousness which has been lacking to date.
"At such a critical juncture, we need someone who is detail focused and sensitive to the complexity of the challenges ahead.
"In short, we need a statesman, not a showman."
Green Party NI leader Clare Bailey said: "Boris Johnson may have been selected as the next prime minister by the Tory Party but has no mandate from the people.
"This new prime minister is intent on a hard Brexit. The man who compared a border on the island of Ireland to the boundary between Islington and Camden cares little about our economic, social and political future."
The head of the Presbyterian Church in Ireland urged Mr Johnson to take a "keen and personal interest" in the ongoing political talks to restore devolved government at Stormont.
Numerous rounds of talks since the collapse of the Assembly in January 2017 have failed to reach agreement.
Dr William Henry has written to Mr Johnson asking him to "actively encourage those involved to go the extra mile".
"The absence of devolved government continues to affect the lives of many of the most vulnerable and marginalised people in our society," Dr Henry said.
"Courageous and compassionate leadership is required to both consolidate, and build upon, the progress already made during the inter-party talks."