It really doesn't make a difference for the 2 phrases you chose. "John, let me introduce you to Alexander" would be the best. After that you could say, "Alexander, this is John."
I read in an etiquette book one time that a girl/woman should never be "presented" (as in "may I present..." which is the most formal of introductions) to a man, but since both of the people in this example are both men (I'm assuming), you shouldn't have to worry about order.