The Italian's current contract expires at the end of Ireland's Euro 2012 campaign and calls for him to be awarded fresh terms have grown since the Republic booked their place at the finals.
The Football Association of Ireland confirmed that they were planning to hold talks after qualification was secured through the play-offs.
Discussions have progressed positively since then and Trapattoni says an agreement has now been reached.
"I will be staying, it is agreed but it is not signed yet," he said.
With Ireland set to learn their group on Friday, Trapattoni admits there are a couple of nations he is looking to avoid.
He said: "I want to avoid Germany because they are one of the best teams in the world and England because of the emotions tied up with a game against them for Ireland."