Northern Ireland’s main political parties have agreed to a deal that will lead to the restoration of the power-sharing government in the region following its collapse three years ago.

The Northern Ireland assembly will sit on Saturday at 1pm and elect new officials including the first minister.

On Friday evening, Sinn Féin confirmed that it would back a deal promoted by the British and Irish governments which included plans to put Gaelic on a par with English, its leader, Mary Lou McDonald, announced. The SDLP also said it would support the agreement.

McDonald said: “We now have the basis to restore power sharing, and we’re up for that.”

She confirmed that the party would nominate ministers for a new power-sharing executive and said Irish language activists should “take heart” over the provisions for Gaelic contained in the new deal.

She added that Sinn Féin was “committed” to Irish reunification efforts and to making sure people across the north-south divide enjoyed the same rights.

The Democratic Unionist party leader, Arlene Foster, called the deal “fair and balanced”. She conceded there will be parts of the deal that will be challenging for the people that she represents. “But overall and on the whole I feel that it’s a fair and balanced deal … I think people will note that whilst there is a recognition of the facilitation of Irish language, there is also very much a recognition of those of us who are Ulster British and live here in Northern Ireland as well, and there is many mechanisms to strengthen the union.”

Foster said the Northern Ireland assembly will sit on Saturday when a new speaker and a new first minister and deputy first minister will be appointed, as well as the other ministers of the executive.

She also said work will be done to improve her party’s relationship with Sinn Féin following three years of suspension of the devolved institutions.

Both parties were threatened with fresh assembly elections if they did not agree a deal by Monday. With both suffering significant losses in the UK general election, that was not an attractive prospect, particularly as the centrist Alliance party doubled its share of the vote on 12 December.

The public had also lost patience with politicians in the backdrop of one of the worst health crises in the region, with the first Royal College-backed nursing strike in a century. McDonald said: “The first action we believe of the incoming executive must be to deliver pay parity to health workers.”

It is understood that the DUP will get three ministries and that one will be headed by the MEP Diane Dodds, possibly education. Sinn Féin will run two, while the SDLP, cross-community Alliance party and the Ulster Unionists will each control one ministry.

At the core of the deal proposed by the British and Irish governments is the creation of two new “language commissioners” as part of a cultural plan to put Gaelic on a par with English while protecting Ulster British culture.

Earlier on Friday, the DUP and Sinn Fein appeared to have accepted the New Decade, New Approach paper put forward by the Northern Ireland secretary, Julian Smith, and the Irish deputy prime minister, Simon Coveney.

Sinn Féin’s ruling executive met at lunchtime to debate the details of the agreement, expressing some concerns over what kind of “veto powers” a unionist first minister might exercise over the commissioners who would have some legal powers to recommend or enforce policies such as dual-language street signs, but it appears those concerns were addressed.

Smith welcomed the return of power sharing. He tweeted: “A devolved government can now start delivering the reforms needed in our public services. After three years, it’s time to get back to work – for the people of Northern Ireland.”

Jeremy Corbyn tweeted: “I congratulate those in Northern Ireland who have worked to reach agreement to allow a return to power sharing at Stormont. The Good Friday agreement and peace process in Northern Ireland is a proud Labour legacy we are committed to support and protect.”

Speaking to reporters in Dublin, Coveney said: “History is being made today. We now have confirmation from the two largest parties in Northern Ireland that they both are committed to re-entering an executive and establishing a functioning Stormont again.”

In comments that came before the SDLP announcement, he added: “Of course, that is not the end of the story, as we want this to be an all-party executive, so I hope that the Alliance party and SDLP will also be able to join Sinn Féin and the DUP in that new executive.”

The SDLP leader, Colum Eastwood, said it was time to get down to work and deliver for the public. “We have had big commitments from the two governments and other parties to ensure that the things that we are concerned about actually get done in this executive,” he said. “That’s why we have taken the decision, as a party, to go into government to make sure that we can deliver for the people we are concerned about. We will go in, probably sceptically, but we will go in and we will do our best to deliver for the public.”