The Vorlon Empire was the region of space under the control of the Vorlon race.
As with all things Vorlon, next to nothing is known about the Empire's governmental structure with no mention ever being made to a specific governing body or head of state, though it's known to have exited in one for or another for at least a million years. 
Vorlon space accounts for a significant stretch of the galaxy though no expedition into this region, by any race has ever returned. At the time the Vorlons claimed the expeditions had met with unfortunate accidents, and suggested no further missions be attempted.   
Official contact between the younger races and the Empire has been infrequent, with the first contact with the Minbari occurring during the First Shadow War, along with the arrival of Valen and his Great Battle Station.  After the war the Vorlons appeared to go back into seclusion and had no official contact with the Minbari until the 2240s, when Kosh Naranek and Ulkesh Naranak approached Chosen One Dukhat in secret. By this time the Vorlons were thought of my most Minbari as almost mythical beings, consigned only to ancient legends. During that period it appears that only Dukhat himself and Anla'Shok Na Lenonn were aware of the Vorlon's presence aboard the Valen'Tha, a fact even the Grey Council were not privy to. After Dukhat's death Satai Delenn became the third person told of their presence. Following the end of the Earth-Minbari War, the Vorlons initiated contact with the Earth Alliance via remote transmission and agreed to send a representative to Babylon 5 and with the arrival of Ambassador Kosh in 2257 came the first documented meeting between Humans and a Vorlon.