The details on Paul's death are not very well-recorded, so it is uncertain the exact date and details of his martyrdom.
Paul had lived as a Christian missionary for many years, going on three missionary journeys, and escaping death more than once. He had been imprisoned in Rome after being accused by some Jews of having brought Gentiles into the Temple. He appealed to Caesar on the grounds of being a Roman citizen, and as a result was allowed to remain in Rome to be tried instead of being sent to Jerusalem.
His trial is assumed to have ended in his acquittal sometime around 65 after being held for several years, at which point it seems he went to Macedonia. Upon his return to Rome, he was arrested once again and imprisoned. Because he was a Roman citizen, he received a different punishment than some other criminals of the time (who were often crucified), and was beheaded between 66-68 AD at Aquae Salviae, which is now known as Tre Fontane.
Legend says that his head bounced three times, and a fountain sprung up at each stop – hence the name Tre Fontane, or Three Fountains. His body was taken about two miles away to be buried in land owned by a friend, where the Basilica of St. Paul Outside the Walls was later built.
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"The tradition is, for now Paul fails us, that Paul, as a Roman citizen, was beheaded on the Ostian Road just outside of Rome. Nero died June, 68 A.D., so that Paul was executed before that date, perhaps in the late spring of that year (or 67). Perhaps Luke and Timothy were with him. It is fitting, as Findlay suggests, to let Paul's words in 2Timothy 4:6-8 serve for his own epitaph. He was ready to go to be with Jesus, as he had long wished to be (Philippians 1:23)"
Lastly, the following quote regarding the death of Paul was taken from the Smith's Bible Dictionary by Dr. William Smith, article "Paul" :
"This epistle, [2Timothy] surely no unworthy utterance at such an age and in such an hour even of a St. Paul, brings us, it may well be presumed, close to the end of his life. For what remains, we have the concurrent testimony of ecclesiastical antiquity, that he was beheaded at Rome, about the same time that St. Peter was crucified there. The earliest allusion to the death of St. Paul is in that sentence from Clemens Romanus, . . . which just fails of giving us any particulars upon which we can conclusively rely.
The next authorities are those quoted by Eusebius in his H. E. ii. 25. Dionysius, bishop of Corinth (A. D. 170), says that Peter and Paul went to Italy and taught there together, and suffered martyrdom about the same time. This, like most of the statements relating to the death of St. Paul, is mixed up with the tradition, with which we are not here immediately concerned, of the work of St. Peter at Rome.
"Caius of Rome, supposed to be writing within the 2nd century, names the grave of St. Peter on the Vatican, and that of St. Paul on the Ostian way. Eusebius himself entirely adopts the tradition that St. Paul was beheaded under Nero at Rome.