"It was strange, because as soon as I joined (Twente) I knew we had the draw coming up," said McClaren, who was sacked as England coach last season.
"I expected one of the English teams. I think fate deals you certain cards and it has dealt us this draw.
He added on Sky Sports News: "I think of all the teams we could have had, that is the toughest - or one of the toughest.
"In one respect it's a tough draw for us; on the other it's now an opponent we know very well, not just myself, everyone in Holland knows the Premier League well so Arsenal will be no strangers to us.
"This is a reward for a great achievement last season in reaching this stage, to get one of the big teams.
"It will be a once-in-a-lifetime experience that doesn't come along that often. I'm sure the fans will be delighted."