The New Testament gives us no indication as to how or when the Apostle Paul died. The Book of Acts ends with Paul under house arrest in Rome (approximately AD 60), where Luke tells us he spent "two whole years at his own expense" (28:30). The great question is whether or not Paul was brought to trial and executed at the end of his imprisonment, or released after those two years only to be executed in Rome a short time to a few months up to a couple of years later. (Did he get to Spain in the intervening time?)
Church tradition is unanimous that Paul was executed under the persecution of Nero, although some accounts say it took place while Nero was away from Rome and that the order was given by the prefects of the city. The tradition also asserts that Paul was beheaded, which seems likely given that he was a Roman citizen and would have been spared the shame and the agony of crucifixion.
He was buried not too far away from the traditional site of his execution. His tomb was a place of pilgrimage early on, perhaps even shortly after his death. The Emperor Constantine built a basilica over his tomb, and in the fourth century the Emperor Theodosius ordered a second basilica to be built on the site as well.
The tomb of St. Paul has now been discovered by archaeologists in basically the location that has been marked by an altar. The only question is whether or not the remains in the sarcophagus are in fact those of the great Apostle. Pope Benedict XVI allowed for the drilling of a small hole in the sarcophagus (which is dated from at least AD 390) in which a probe was inserted. Some tiny bone fragments were removed and carbon dated. The person in the sarcophagus lived in the first to the second century AD.
The pope has stated that this seems to confirm the unanimous tradition. He is right. But the most that can be said from the carbon dating alone is that the individual buried there lived in or around the Apostle Paul's time-- nothing more. If it were possible to open the tomb then there might be enough remains to discover more about the person buried there. Was the person male? Approximately what was his age at the time of death? Most significantly of all, was he beheaded? It is doubtful that the pontiff will allow that kind of disturbance of the tomb. According to tradition, Paul's head is not with his body. The skull or at least portions of it are at the St. John Lateran Basilica in Rome.
On scientific grounds alone it cannot be confirmed nor denied at this point that St. Paul is buried in that spot, but the historian has more evidence to go on. The tradition that Paul was buried there is not confused. Surely, Paul's contemporaries would have known where he was buried. The only question somewhere along the way through the decades is whether or not that spot was somehow forgotten and another incorrect location took its place, but there is no evidence from the historical records we have that such a thing happened. So, one would have to argue that Paul's contemporaries got his burial location wrong right from the beginning. But is such a possibility believable?
Of course, if indeed the remains of Paul have been found this does nothing to "prove" the truth of Christianity, although some will want to see it in that way. All it will demonstrate is what we already know-- Paul of Tarsus actually lived and was a follower of Jesus and later on in his life, he went to Rome and was executed.
Nevertheless, that the tomb of Paul may have been found is quite intriguing and exciting.