It's well-known that intellectuals in the West have accepted a spherical Earth since antiquity, but I'm not sure how long it took for this to become common knowledge, worldwide. So a more concrete answer is possible, I'll say it's "common knowledge" if >50% of adult humans know it.
Earlier, I asked this question regarding what pre-Columbian Americans thought about the shape of the Earth. There is no evidence that any society arrived at the idea of a spherical Earth, though of course, it's hard to prove a negative. I also read this thread, which explains that most Chinese scholars favored the flat Earth model before the 17th century.
My hypothesis: the true shape of the Earth was not well-known before the 19th century. I have two points:
Public education. While it had been the consensus in academic circles for centuries beforehand, the lack of public education meant that this knowledge did not reach most of the public. In the 1800s, a large number of countries began mandating formal education, starting in Europe and soon spreading to the Americas and the Asia-Pacific.
Population. The European public was early in learning about the shape of the Earth, but before the industrial and agricultural revolutions of the 1800s, Europe had only a small slice of the global population. In 1500, Europe's population was 18% of the world total. By 1913, it was a more significant 28%. Many high-population regions, such as China and SE Asia, were among the last places to accept the spherical Earth model. West Asia, where the idea was popular since antiquity, has a relatively small population.
I'm not completely convinced yet, and I've also heard that nearly all people have known the shape of the Earth since prehistory. The argument is that it's too obvious not to see; for example, you can watch mountains and other tall features disappear below the horizon as you move away from them. A reason to be skeptical about this: it's hard to then explain why so many early religions (e.g. ancient Sumerian religion) describe a flat Earth.