The leader Eamon Ryan will now request a meeting with the two larger parties.
The Taoiseach had said earlier this week that he was keen to discuss the possibility of forming a Government along with the Green Party, however there were some issues surrounding how a seven percent reduction in greenhouse emissions.
The Green Party say they have got approval from the parliamentary party on developing a programme for government.
In a statement, it says that it will require the support of two-thirds of all of its members.
No legislation can now pass, until a Government is formed, with Fine Gael and Fianna Fail needing the support of independents and another party.
The Taoiseach's welcoming the Green Party's decision to start negotiations on a Programme for Government.
Leo Varadkar says he looks forward to constructive discussions starting in the coming days.
He says Ireland needs a stable government to manage the remainder of the Covid emergency and to rebuild and renew our society and economy over the next five years.
He says working together they can help to deal with the challenges facing Ireland, including getting people back to work and re-opening businesses.
The Fianna Fáil Leader has welcomed the confirmation that the Green Party will now enter into formal negotiations on a Programme for Government.
Micheál Martin says as the country faces into a very uncertain future, it is critically important we have a solid and stable Government in place.
He says he wants the parties to protect people and ensure the country's economic recovery after Covid-19 is started as soon as possible and is built on fairness.
He says there's important legislation that needs to be passed to allow Irish businesses to access finance and there needs to be a government in place to do this.