This hairstyle dates back to ancient Egypt, where dreadlocks appeared on Egyptian artifacts. On archaeological sites around Egypt, mummified remains of ancient Egyptians were dug up and found to have their hair dreaded. There is even a reference that recounts deadlocks in the Old Testament. The tale of Samson and Delilah talks about dreadlocks in which a man's potency is directly linked to "the seven locks on his head". The first writing about dreadlocks comes from India in the Veda scriptures dated to 1800 BC. Many cultures wore dreadlocks in the early ages, the Germanic tribes, the Greeks, the Naga Indians and even King Tut had dreadlocks, which are still intact to this day.

The reason the hairstyle is as popular as it is today is because of the Rastafarian movement that was born in the 1930s. Pop icon, Bob Marley sported deadlocks and brought them into mainstream culture, along with the philosophy of Rastafarian culture.
Information from:
http://www.knottyboy.com/learn/dread_history/
http://www.howtodread.com/dreads.html