Tsuna has been named the true successor of Vongola IX by the ninth himself, and was also supported by the head of the CEDEF, Iemitsu, his own father. Tsuna then proves his worth as the tenth boss by defeating Xanxus, and winning the battle for the Vongola Rings, as per family tradition. In the future, Tsuna undergoes "The Trial", which is an ancient tradition that each Vongola boss undergoes. After showing his resolve, Tsuna is recognized as the true Vongola X by the former bosses of the Vongola Family.
Although, since Timoteo believes he can still continue to run the Vongola Family for a while longer, Tsuna has yet to take power as the tenth boss during his current time (the time before he is transported into the future).
** Spoiler Alert!!! click to hide or show**
In the alternate future, Tsuna is revealed to have died. However, he was revered as a great boss, as his prowess in battle and his dedication to his family were known throughout the Mafia world.