Letters from Hamza, then aged 22, have been declassified and have been revealed by Ali Soufan, the ex-FBI agent.
Hamza, who was once tipped to take over leadership of al-Qaeda after his father, allegedly wrote the notes to his dad.
The letter read: “Every look… every smile you gave me, every word you told me, I consider myself to be forged in steel. The path of jihad for the sake of God is what we live [for].”
Bin Laden senior was killed by US Navy Seals in 2011 after being at the top of the US most wanted list for a decade.
US Navy Seal Team Six killed Bin Laden in Abbottabad, Pakistan, on May 2 in 2011.
Dozens of letters written by him to his family have since been released to the public after his hideout was raided for intelligence.
Hamza, now believed to be 28, committed himself to the terrorists’ cause within the letters.
Since then, he has openly threatened terrorist attacks in London, Washington and Paris.
Mr Soufan said plans for Hamza to take control were put in place when he was still a child.
In 2015 Al Qaeda released an audio message of Hamza.
Since, he has released four messages calling for murder in the West.
The ex-FBI agent said:
“He was a poster kid for Al Qaeda… and for members of Al Qaeda, who were indoctrinated with these propaganda videos, he means a lot to them.”
Mr Soufan said:
“He’s basically saying, ‘American people, we’re coming and you’re going to feel it. And we’re going to take revenge for what you did to my father… Iraq… Afghanistan.’ The whole thing was about vengeance.”
This year, in January, Hamza was placed on a US state department terror watch list.
As his father was, Hamza was classed “specially designated global terrorist”.