The answer to your question has roots in a torture mechanism used in the process known as breaking on the wheel. This implement combined, in an odd way, with the common European belief that storks were lucky, yielding the idea that storks could be credited with the arrival of a baby.

My Introduction to Folklore describes how this process worked, so I will excerpt it here:

One common practice related to childbirth resulted in a traditional fict of western culture. A woman was in jeopardy during birth because a host of supernatural creatures might attempt to abduct her and leave a replica in her place that would appear to be her corpse. To avoid such a fate, people ushered children outside and sealed the house. When the birth was complete, the doors and windows could be reopened and the children returned. There was a need, however, to explain the arrival of the infant.

Parents wanting to avoid the topic of conception and childbirth relied on the fact that the only opening to the house was the chimney. Coincidentally, European peasants had observed that storks nested on the little-used gallows or “Catherine” wheel in towns. These looked like wagon wheels positioned horizontally on tall poles, and storks found them a safe place to nest. The birds were regarded as good luck, so it was not uncommon for people to construct a similar wheel on top of their roofs to attract storks. When children asked about the origin of the infant, it was easy to suggest that it had arrived by way of the chimney and that the stork had accomplished this deed.

So, in answer to your question, the traditional association with storks with the arrival of an infant is European, and consequently, North American. I hope this helps.