Taoiseach Leo Varadkar met and discussed the Confidence and Supply arrangement with Micheál Martin earlier this evening.
In statements issued this evening, Fine Gael and Fianna Fáil say the teams will be appointed this week.
They will hold their first meeting next week.
Earlier the Fianna Fáil leader said he will not allow the Taoiseach to govern timelines on any talks aimed at extending the agreement.
Leo Varadkar believes a deal could be done by the Halloween break, however Micheál Martin says he will not agree to preconditions.
"I don't want to get into any more timelines, is it this month or that month," Mr Martin said.
"It's going to be a substantive review, it has to be detailed and it has to be substantive.
"I've made my position clear. I'm not going to be governed by timelines.
"The Taoiseach and myself spoke last Tuesday on this. He agreed with me there would be no preconditions and I'm not accepting any preconditions.
"He agrees there shouldn't be any preconditions and that's it."