Ireland are seen as outsiders for success in Poland and Ukraine and face a tough task to progress from Group C, having been drawn alongside world and European champions Spain, as well as Italy and Croatia.
But Giovanni Trapattoni's team are unbeaten in their last 14 games and Keane feels that they can continue that form going into the tournament.
"If you look at our record over the last couple of years it's been very, very good," he told RTE. "We're coming into this competition with a lot of confidence and belief that we can certainly get out of this group.
"People fancy Spain and Italy because they are two massive nations to get out of the group. By no means is it going to be easy, we know that. It is one of the toughest groups.
"I've been with the lads now for the three weeks. With the belief that we have in the squad for the last three years, there is no doubt in my mind that these players are going into this competition believing that they can get out of this group."
Ireland kick off their Euro 2012 campaign against Croatia on Sunday, and Keane recognises how important it is that they pick up maximum points.
"I think the start of any competition is important and certainly the first game. We are playing a team that people see as a little bit similar.
"We know they have grown as individual players and collectively as a team since [Slaven] Bilic took over as manager. They have become a stronger and even better team.
"They have someone like Luka Modric, who I know very, very well. I've been speaking to him over the last couple of days, having a bit of banter with him.
"I look forward to playing against him and hopefully after the game shaking his hand with three points in the bag."