I would say that the major global impact of the colonization of the Americas was on the balance of power in Europe. Because European countries were dominant, this also affected the balance of power world-wide.
For example, the earliest colonization of the Americas helped increase the power of Spain. Spain's colonies from Mexico on to the south were immensely rich. They produced such things as the huge amounts of silver from what is now Mexico and the Potosi mines in Peru. These sums of money helped pay for Spanish wars all over Europe.
Later on, colonization in the Americas led to an increase in British power. This happened as what is now the United States became a valuable source of trade (as did Britain's Caribbean territories). This change led to competition worldwide, such as was seen in the 7 Years War.
So colonization of the Americas impacted the global balance of power as various countries' American colonies helped to increase their wealth and power.