It depends on how you define a "graveyard". Many times people are just buried, and I believe Richard III was an example of this. He was not really taken to a specific grave and buried in a cemetery the way we think of it, but merely interred "with no funeral solemnity" (Ashdown-Hill, John; David Johnson; Wendy Johnson; Pippa Langley (2014). Carson, Annette, ed. Finding Richard III: The Official Account of Research by the Retrieval & Reburial Project. Horstead: Imprimis Imprimatur, p. 8). Sometimes you have a mass grave at the site of a battle, and sometimes you just have people buried in a place near where they died, and it may not have been a "graveyard" officially.

The practice of burying the dead has existed since well before the existence of the homo sapiens species. Neanderthals were burying their dead in caves like Kebara Cave in Israel around 60,000 years ago. This cave also housed a Natufian (11,000-12,000 years ago) burial ground containing 17 individuals. Therefore, people interred their dead in specific locations at least that long ago.

Ancient Lower Egypt buried their dead with a single pot in a small round pit in the Predynastic periods (~4500 BC). I know of Iron Age graveyards outside settlements in the Near East (~1000 BC), and some from the Bronze Age (~2000-1200 BC). I'm not an expert on funerary practices, so you may want to see if there's an expert here or on /r/askanthropology who can give you a better idea.

But basically, burial has been around for a very long time. In the earliest days, it was most likely out of convenience, in the floor of the cave, or out of the way. But, in the Bronze Ages (and probably earlier) it became more popular to have a specific area in which to inter the dead. Note that it was not adopted everywhere at once, and some cultures would process their dead in different ways (some practicing interment in the floor, others interring in a cave or other place outside the settlement, others practicing cremation).

It's hard to put a beginning date on it, because so many things haven't been excavated in these early time periods. But certainly by the Bronze Ages it was common practice to inter in a specific place. Perhaps even earlier than that, given some apparent Neolithic things.

Er in the case of Richard he was buried in the floor of a church that was demolished about 75 years later with the graves not relocated.

That really depends on which cultural group, regional group, time period, or religious adherence you are examining. We even have evidence of h. neanderthalensis burying their dead, so it is clearly a practice that has existed throughout time. Different cultural groups had/have different ways of treating the dead, so to answer you question - narrow your focus to see the origins of burial patterns throughout time and space!