It could mean the Fine Gael leader Enda Kenny returning as Taoiseach (Irish Prime Minister) next week, subject to ratification.
Mr Kenny and Fianna Fáil leader Micheál Martin are expected to talk over the weekend.
The parties are the two largest in the Republic of Ireland.
They met on Friday, with policy issues mentioned in the framework document including public service pay and the housing sector.
Their respective parliamentary parties will consider the document and have to ratify it.
It will also need to attract the support of Independent TDs (MPs) for Mr Kenny to become the first Fine Gael Taoiseach (Irish prime minister) returned in successive elections.
The Irish parliament is due to meet again on Wednesday, it is unclear whether everything will be in place by then, as it is a bank holiday weekend in the Republic of Ireland.
"We have an agreement," acting transport minister Paschal Donohoe told journalists after weeks of talks between the two parties.
He said a significant amount of work would be done over the coming days, before a draft of the agreement is put before the Fine Gael parliamentary party.
Fianna Fáil's Michael McGrath told the Irish state broadcaster RTÉ he was "pleased and relieved" to have concluded talks with Fine Gael.
He said the Fianna Fáil parliamentary party would be on standby over the weekend to meet once the final document agreement had been drafted.
Under the deal, Fianna Fáil will not bring the government down in confidence motions or object to reshuffles.
With all other parties in the Republic of Ireland's fractured parliament refusing to join Fine Gael in government, the centre-right party needs to secure the support of some of the 14 independent TDs (MPs) it has been in talks with for weeks.
Fianna Fáil campaigned against the outgoing Fine Gael government in the recent election.
Following February's election, Fine Gael had 50 seats, Fianna Fáil 44, Sinn Féin 23 and the Labour Party got seven.
But no party was able to form a majority government and TDs have failed to elect a leader on three previous occasions.
Fianna Fáil and Fine Gael have dominated Irish politics since the early 1930s but they have never been in a formal coalition.
Fianna Fáil has agreed to support a minority Fine Gael government over three budgets in the Republic of Ireland.