Reasons for Migration
Voluntary Migration
During this time period in history, the Industrial Revolution occurred, bringing about the automation of labour, and therefore, increased job opportunities. The rising industrial and agricultural centers attracted many immigrants seeking a better life. This, combined with improved transportation, made industrialized societies a magnet for voluntary immigrants. Colonies also provided opportunities to those in the homelands, leading to some migration from homelands to colonies.
Many Chinese migrated to the US during the 1800s, and were vital to the construction of the Transcontinental Railroad. For the most part, they migrated voluntarily.
The Global Capitalist Economy
The Atlantic slave trade in the Americas came to a close during the Modern Era, in 1888 after its abolition in Brazil. The slave trade provided some benefit, however, as the economy fluorished due to the plantations fueled by slaves in the colonies. It can be said the economy somewhat relied on these slaves for a time, that the growth of industrialization was connected to colonial slavery.
Indentured servitude became common in American colonies around the time of slavery. In a couple of colonies, indentured servitude became part of a system known as the Headright System. It facilitated migration across the Atlantic of servants to come work for masters in the colonies/states. Technically, it wasn't slavery as the servant was paid at the end of their contract through "freedom dues". However, it ended up as a system of indentured servitude. Servants lived to the end of their contracts less than half of the time, and when they were finally freed they would receive low-tier land. However, it should be said that this increased migration between Europe and the Americas and helped develop the colonial economy.
During the 19th century, Chinese workers were imported into the Americas. They were vital to the construction of the Transcontinental Railroad, arguably one of the most important projects of the 19th century in the USA. Much of their labor in the USA was involuntary, yet they contributed massively to the development of Western territories. It was elsewhere in the Americas that their work went deep into involuntary servitude territory, however. They did a lot of economically-important work in silver and guano mines in the Caribbean, but were frequently forced to do it. Most of these "coolies" as they were called did this against their will. Frequently, they were kidnapped from wherever and forced into labor, not unlike the slave trade.
Temporary Migration
It was not uncommon for Italian immigrants to temporarily move to Argentina, looking to earn money to send home to Italy. Many Italians passed through Argentina, arriving at the beginning of the harvest, and leaving at the end, earning the name of "golondrina". In response, Brazilian planters only allowed family migrations, which were more permanent.