A lot of popular history, and even my own undergraduate courses twenty years ago strongly imply the Han Chinese culture was very inward-looking, largely unconcerned with other cultures except to keep invaders at bay. When the Chinese Empire expanded its territory, it was mainly during the rule of non-Han dynasties like the Yuan and Qing (Tang being the notable exception). Han dynasties seemed content to rule over a mostly Han populace within the borders originally united by the Qin/Han dynasties. This line of thinking will bring up events like the Ming dynasty court ending Zheng He's far-reaching expeditions as examples of this mindset.
However, in the last century and a half, Han Chinese have emigrated to almost every corner of the globe, and appear to be successful almost every where they settle. Chinatowns are found in major cities all around the world, many small business are owned and operated by Han Chinese, and later-generation immigrants excel in higher education and professional vocations. At least, this is the popular perception; e.g. the "model minority".
What caused this cultural shift from isolationism to successful integration?
Imperial China was not nearly as isolationist as most historical narrative would have you believe, and even the isolationism that did exist was on the part of the government rather than the population. Emigration to foreign lands had being a fact for coastal Chinese peoples for over half a millennia now.
Beginning in the Song dynasty Chinese traders and merchants started to regularly travel to Japan, Philippines, Southeast Asia and as far as India. Starting in the Ming dynasty Chinese traders started to settle down in places they traded in, every wave of dynastic change in China also produced fresh wave of refugee emigrants. Those emigrants, like those who first came to America, were at first speakers of the Fujian dialect and later emigrants were Cantonese and other peoples from coastal southern China.
By the 1600s around 20-30,000 Chinese lived in Spanish Manila in the Philippines. Over 80,000 lived in Jakarta and other towns in Indonesia. Ayutthaya in modern day Thailand also contained tens of thousands of Chinese. Most of them were merchants, accountants, ship crews and craftsmen. By 1800, there were perhaps altogether one million ethnic Chinese immigrants in Southeast Asia: living under a variety degree of suspicion by their host countries, often confined to residing in designated parts of cities.
And it wasn't just Southeast Asia the Chinese settled, there were Chinese immigrants as far as Mexico City in the 1600s. They traveled there via Spanish Galleons carrying trade goods from Asia, and served as Shopkeepers, barbers, textile workers and other professions. Some even made it as far as Brazil to become gold miners. Hundreds of Chinese settled in India as well.
Most of those Chinese underwent assimilation over the course of centuries, partially because they were prominently male and thus had to intermarry into their local societies and gradually over time stopped identifying as Chinese altogether or created some form of mixed identity. Examples include Peranakans in Indonesia and Chinese Mestizo in the Philippines.
In other words, the pattern of Chinese emigration did not begin in the late 1800s, but rather was a continuation and intensification of a trend which began centuries ago, enabled by the environment of the first great wave of globalization.
Source: Chinese Migration and Settlement in Southeast Asia Before 1850: Making Fields From the Sea by Craig A. Lockard
/u/desoulis and /u/parksunjung already gave very good replies and I want to point out a major issue in the historiography. There is tendency to read surviving records too literally. And a great majority of surviving records were written by courtiers in the court of the emperors. The work done in Cambridge's History of China is fantastic but they often lack critical analysis. This is how the myth of Zheng He came to be, that he had oceangoing vessels of size so large they violate limits of mechanics.
We are now starting to be able to clearly see the conundrum between an isolationist imperial policy and a flowering maritime trade by "Chinese merchants". One of the things we need is to distinguish the use of "China" and "Chinese" to mean the people, the nation, the history, the culture, with no resolution.
Of course, for some parties today it is very expedient to abuse the term.