The limestone burial box for bones - called an ossuary - bears an inscription reading "James, son of Joseph, brother of Jesus" in the Aramaic language.
The writing style, and the fact that ossuary burials were only practised by Jews between 20 BC and AD 70, put the find squarely within the time of Jesus and James, says Andre Lemaire, a French specialist in ancient inscriptions.
Writing up his findings in Biblical Archaeology Review, a US journal, Mr Lemaire says it is very likely that the inscription is an authentic reference to Jesus.
Experts do not doubt the existence of Jesus, but almost everything known about him comes from the New Testament.
There are no other verified artefacts from the first century.
Well-known brother
Although all three names were commonplace in Jerusalem during that time, Mr Lemaire estimates that there must have been only about 20 Jameses with a father named Joseph and a brother named Jesus.
Moreover, it was quite unusual to name brothers on such burial boxes, suggesting that his brother must have been unusually well known - which Jesus certainly was.
Two scientists working for the Israeli Government's Geological Survey have examined the box's surface patina and the inscription at microscopic level.
According to the journal, they reported last month there was "no evidence to detract from the authenticity".
They also confirmed that the limestone originated in the Jerusalem area.
Help from a historian
But there is no way to prove conclusively that the Jesus named on the box is Jesus of Nazareth.
Despite this, Mr Lemaire has used testimony from the first-century Jewish historian Josephus in an attempt to date the find more precisely.
Josephus recorded that "the brother of Jesus the so-called Christ, James by name" was stoned to death as a Jewish heretic in AD 62.
Had his bones indeed been placed in an ossuary, that would have happened the following year, dating the inscription to around AD 63 - about 30 years after the crucifixion.
The owner of the box - an unidentified private collector in Jerusalem - did not realise the significance of the object until it was examined by Mr Lemaire in spring 2002.
He or she has no plans as yet to put the box on public display.