The word tie-dye encompasses a wide variety of dye processes. I've defined it as any dye process in which a pattern (no matter how crude) is produced by a resist from folding, twisting or tying material in any way you can think of. Some type of tiedye process was probably used shortly after the first fabrics and dyes were invented. I'm sure it didn't take very long for someone to discover that twisting or scrunching material before it was dunked in the berry juice produced a pattern, and from there it was a short step to adding some string or vines or something.
Since fabric is perishable we don't have direct evidence of the earliest dye arts. Archaeologists have found a variety of stamps that may have been used for printing fabric 5,000 years ago in Mesopotamia and India. Some of the stamps are rocker shaped, some are cylinders, and some are flat with a handle on the back, indicating a variety of uses. I would bet that if they could block print, they had already tiedyed. Actual resist-dyed mummy cloths have been found from 1000 BC in Egypt. We think that dyeing techniques traveled along trade routes from India to Egypt.
There is also a rich tradition of tie-dye "shibori" in Japan where dye techniques were introduced from China around 400 BC. Shibori is still practiced in Japan and the United States. About 400 AD, Indian traders introduced dying techniques to Java where the art of Batik was developed. Plangi, tiedye, and a sewn version "tri-tik" also flourished in Indonesia.
Tie-dye has been practiced extensively in Africa, especially in Nigeria. I have also personally heard that there is now a tradition of tie-dye on the West Coast of Africa that uses synthetic dyes and patterns similar to ours -- if anyone has any more information about this please let me know.
In the Americas, Pre-Columbian Peru stands out for its tradition of fabric art in which tie-dyes play a central role.
The So-called Modern World
Many types of tiedye are still used today for clothing, backgrounds for screen printing, sheets, tapestries, tees, and table covers. Often whole garments are dyed, but many items are also made from material that has been previously dyed. Our particular type of tie-dyeing was not possible until the invention of fiber reactive dyes in 1956. Until then, dyes had to be applied hot or with strong chemicals. Procion, the principle fiber reactive dye, can be applied cold and can be dripped on, which allows more than one color to be applied without reprocessing. Procion dye is also extremely colorfast. I personally started tiedying in 1978 when I went to work for "The Tiedye Company" on a community in Tennessee called "The Farm". The Tiedye Company had just been started by Charlotte Gabriel, who should get credit for developing many of our basic techniques, and in particular for inventing the star pattern.