The short answer is: It's fuzzy and no one really knows.

The long answer is: First we have to define what a "vampire" really is. Is it any dead body that has risen from the grave and seeks to harm the living? Then the common cultural phenomenon of the zombie would also be a vampire. Or is it that the additional trait of "drinking blood" is needed?

Drawing from my class notes, I would say that in the 13th and 14th century in Bulgaria, dead with stakes through their heart would most likely have been considered "strigois". Strigoi is akin to the German "Wiedergänger" - "someone walking again"; i.E. a dead risen from the grave.

The belief in these strigois, harmful spirits of the dead out to harm the living, sometimes taking a form very closely related to our popcultural vampire is considered to date back to the Dacians who settled in the Balkans area (disclaimer: When I say Balkans in this answer, I mostly refer not to the modern geographical Balkan area, but rather to the cultural region that reaches from Romania to Northern Greece and Slovenia) during the Greek and Roman eras.

The first documented case of supposed vampirism only occurs in the 18th century though. It is the case of Peter Plogojowitz, a Serbian peasant living in Istria living in a region that went into Austrian hands after the Peace of Passarowitz. The Austrians were interested in their new lands and when word of the case of a dead supposedly returning to haunt the village reached the authorities, they sent a clerk to the village. And this proved to be a lucky break for us historians, because his report has endured time and now we can say that at least in this time, a phenomenon very similar to our idea of a vampire existed. The report states that the villagers claimed to have opened the grave and found the dead body with fresh blood on his lips. Then they asked for permission to burn the body and drive a stake through its heart. So we have a lot of common traits of our modern vampire picture.

The original report can be accessed here, but sadly only in German

A couple of decades earlier in 1645, Father Leo Allatius, a greek theologican in the Vatican, writes about occurrences on the island of Chios:

"For very often, inhabiting this body, he [the devil] comes forth from the grave, and going abroad through villages and other places where men dwell, more especially at night, he makes his way to what so ever house he will, and knocking upon the door he calls aloud by name in a hoarse voice one who dwells within. If such a one answers he is lost; for assuredly he will die the next day. But if he does not answer he is safe. Wherefore in this island of Chios all the inhabitants, if during the night they are called by anyone, never make reply the first time. For, if a man be called the second time it is not the vrykolakis who is summoning him but somebody else."

While this is not as good a document as the Plogojowitz case, it indicates that the legends are very much older and predominant in the Balkan and Greek regions.

So, long story short: The first documented case of this legend is only in the early 18th century, but the mythological background reaches far beyond this. The findings of graves with staked bodies dated to the 13th and 14th centuries enforce this.