The Hokage is the most prestigious position that any Shinobi from the village of Konoha can hold in the Naruto series. This position is reserved for the very best of ninjas who prove themselves to be incredibly powerful, with a keen mind and, most importantly, possess the Will of Fire.
The Hokage is the protector of the village and all the people living within the village are their family. So far, Konoha has seen seven Hokage in the series, however, the ages at which they were elected vary greatly. While some were elected in the prime of their powers, others had to take this position at an incredibly young age.
7 Tsunade Senju
Tsunade Senju is, by far, the oldest Hokage to have ever been elected in Naruto. After the death of Hiruzen Sarutobi, Tsunade was sought out by Jiraiya and, later, she was made the Hokage.
In part one of Naruto, Tsunade is 51 years old, meaning that she was made Hokage at this age. She went on to rule as the Hokage for quite a few years before eventually passing on the mantle to Kakashi Hatake.
6 Tobirama Senju
Tobirama was the Second Hokage of Konoha and he took this position shortly after the death of his brother, Hashirama, in the First Great Ninja War. Tobirama was instrumental during his time as Hokage as he established the likes of the Academy, the Konoha Police Force, and the ANBU, among other things.
He was also one of the worst Hokage in the sense that he ostracized the Uchiha and made sure they suffered. When it comes to age, Tobirama was elected late into his life, and given that the gap between him and his brother isn't that much, he was certainly well into his 30s.
5 Hashirama Senju
Hashirama Senju was the First Hokage of Konoha and a ninja known to be the God of Shinobi. He was incredibly powerful and, having grown up on the battlefield, could take on any threat at any time. Together with Madara, Hashirama ended up creating Konoha and, while Madara was originally supposed to be the First Hokage, Hashirama was elected by the people and because Tobirama wanted it to happen.
At this point in his life, Hashirama was quite old and, given that he was old enough to have a granddaughter, it can be assumed that he was well into his 30s as well, at the very least.
4 Kakashi Hatake
Kakashi Hatake was the Sixth Hokage of Konoha and he took over this position after Tsunade, following the events of the Fourth Great Ninja War. At the end of Naruto, Kakashi was around 31 years old, and he ended up becoming Hokage shortly after it.
It can be safely assumed that Kakashi took over the position of Hokage around the age of 31- 32 years. He ruled as the Sixth Hokage for quite a long time and Konoha was the most peaceful under his reign.
3 Naruto Uzumaki
The 7th Hokage of Konoha, Naruto Uzumaki is actually one of the youngest to ever become Hokage. In Boruto, Naruto is revealed to be 33 years old, however, he ended up becoming Hokage a few years before that. This would mean that Naruto became the Hokage around 29 to 30 or 31 years of age.
While the world is in a state of chaos right now, Naruto is doing exceedingly well as the 7th Hokage. He is the strongest Hokage to ever live and will likely remain the strongest of all time.
2 Minato Namikaze
Minato Namikaze was the Fourth Hokage of Konoha and also one of the youngest to attain this position. He was known to be an excellent ninja, strong enough to be a Kage before even reaching the age of 20. Minato was instrumental in the Third Great Ninja War and it is after this war that he ended up becoming the Fourth Hokage.
He died at the age of 24, however, by this time, he was already the Fourth Hokage for quite a while.
It can be assumed that Minato ended up becoming the Hokage around 20 years of age, or in his early 20s.
1 Hiruzen Sarutobi
Hiruzen Sarutobi is the youngest Hokage to live in Naruto. He became the Hokage in the First Great Ninja War when Tobirama passed on this position to him, after setting himself up as a decoy. Hiruzen graduated from the academy at 12 years of age and, shortly after, the kids were sent off to fight in the war.
It was during this war, which lasted for quite a long time, that Hashirama ended up dying. After Tobirama became the Second Hokage, the many Shinobi of Konoha continued to fight. Before reaching adulthood, Hiruzen had the responsibility of Hokage thrust on his shoulders. While an exact age has not been given, Hiruzen most certainly became the Hokage before reaching the age of 20.