When will be know the results of the constitutional referendum?

Here is the quick answer: The voting takes place on Sunday but the polls don't close until 11 pm local time (5 pm in New York).

After that, the counting will start.

So it won't likely be until sometime early Monday morning in Italy that we know which side won. I suspect will start to get an idea around 3 hours after the end of voting but it could be significantly later, especially if it's close.

What's important to note is that markets will be open when the results hit and that could create a tremendous amount of volatility. Many forex brokers have cut leverage ahead of the result in anticipation of a big move in the euro.

The second event to watch after the results will be the speech from Italian Prime Minister Matteo Renzi. He has said he will resign if he loses. If that takes place immediately after the vote, it willl add to the uncertainty and weigh on the euro.