This article is from the Calendars FAQ, by Claus Tondering firstname.lastname@example.org with numerous contributions by others.
In about AD 523, the papal chancellor, Bonifatius, asked a monk by the
name of Dionysius Exiguus to devise a way to implement the rules from
the Nicean council (the so-called "Alexandrine Rules") for general
Dionysius Exiguus (in English known as Denis the Little) was a monk
from Scythia, he was a canon in the Roman curia, and his assignment
was to prepare calculations of the dates of Easter. At that time it
was customary to count years since the reign of emperor Diocletian;
but in his calculations Dionysius chose to number the years since the
birth of Christ, rather than honour the persecutor Diocletian.
Dionysius (wrongly) fixed Jesus' birth with respect to Diocletian's
reign in such a manner that it falls on 25 December 753 AUC (ab urbe
condita, i.e. since the founding of Rome), thus making the current era
start with AD 1 on 1 January 754 AUC.
How Dionysius established the year of Christ's birth is not known (see
section 2.13.1 for a couple of theories). Jesus was born under the
reign of king Herod the Great, who died in 750 AUC, which means that
Jesus could have been born no later than that year. Dionysius'
calculations were disputed at a very early stage.
When people started dating years before 754 AUC using the term "Before
Christ", they let the year 1 BC immediately precede AD 1 with no
intervening year zero.
Note, however, that astronomers frequently use another way of
numbering the years BC. Instead of 1 BC they use 0, instead of 2 BC
they use -1, instead of 3 BC they use -2, etc.
See also section 2.13.2.
It is sometimes claimed that it was the Venerable Bede (673-735) who
introduced BC dating. Although Bede seems to have used the term on at
least one occasion, it is generally believed that BC dates were not
used until the middle of the 17th century.
In this section I have used AD 1 = 754 AUC. This is the most likely
equivalence between the two systems. However, some authorities state
that AD 1 = 753 AUC or 755 AUC. This confusion is not a modern one, it
appears that even the Romans were in some doubt about how to count
the years since the founding of Rome.