Ireland have been drawn in Group C with three-time winners Germany, Sweden, Austria, Faroe Islands and Kazakhstan.
"I believe it's a good draw. I think we've got a great chance of doing well in the group," he said.
"There is no team we will be afraid of. Naturally, Germany will be favourites, won't they, but we're capable of beating any of the sides in the group so I think we're very pleased, to be fair."
Delaney also revealed that he had spoken to manager Giovanni Trappatoni and said the Italian was satisfied with the draw.
"I've spoken to Giovanni, he's pleased. He's managed in Germany and Austria so has a connection to both those countries."
Ireland missed out on last year's tournament after being denied in a play-off by France, a game made famous for Thierry Henry's handball assist for the goal which sent the French through.