Answer:
Tiberius was at first least likely to succeed Augustus. Augustus' designated heirs was at first Marcellus, his nephew and his daughters husband. When he died in 23 BC, Augustus married his daughter Julia to his close friend and right hand, Marcus Vipsanius Agrippa. They had 5 children of whom 3 were males. These were Gaius, Lucius and Postumus. Postumus was considered a bit retarded and bad tempered so he was out of the heritige line. Gaius and Lucius, Augustus' little donkies, as he liked to tamper them, were the designated heirs. In the mean time, Tiberius had enough of political and military life, so in 6 BC he suddenly retired to Rhodes living a peaceful life helping the local people and bonding with them.
With Tiberius's departure, succession rested solely on two young grandsons, Lucius and Gaius Caesar. The situation became more precarious in AD 2 with the death of Lucius; Augustus, with perhaps some prompting from Livia, allowed Tiberius to return to Rome as a private citizen and nothing more. In AD 4, Gaius was killed in Armenia and, to paraphrase Tacitus, Augustus had no other choice but to turn to Tiberius.
The death of Gaius in AD 4 initiated a flurry of activity in the household of Augustus. Tiberius was adopted as full son and heir. In turn, Tiberius was required to adopt his nephew, Germanicus, the son of his brother Drusus and Augustus' niece Antonia Minor. Along with his adoption, Tiberius received tribunician power as well as a share of Augustus's maius imperium, something that even Marcus Agrippa may never have had. In AD 7, Postumus was disowned by Augustus and banned to the island of Planasia, to live in solitary confinment. Thus, when in AD 13, the powers held by Tiberius were made equal, rather than second, to Augustus's own powers, he was for all intents and purposes a "co-princeps" with Augustus, and in the event of the latter's passing, would simply continue to rule without an interrernim or possible upheaval.
Augustus died in AD 14, at the age of seventy-six. He was buried with all due ceremony and, as had been arranged beforehand, defied, his will read, and Tiberius confirmed as his sole surviving heir.