I am actually working on a master's thesis that partially covers the topic. Mostly what you get is that the system generally started in the middle of the 19th century. Now, the fach system didn't just come together one day, it was most definitely a process of hindsight. The Germans love to organize things and who wouldn't want to do the same to the voice. There are also different versions of the fach system including: German, European, and American. These are the big three. There are a few articles and books that cover these different systems.
"The Opera Singer's Career Guide: Understanding the European Fach System",
by Pearl Yeadon McGinnis
"What the Fach? A beginner's guide to the German Fach system"
by Tiana Malone
Both of the sources talk a little about the history, not much, but a little. The fach system history isn't a very researched topic. There is a lot of research that goes into finding just a little bit of information about this topic.
Feel free to add some more sources on the history. Hope this helps.