Shantanu was no ordinary being. He was Avatar of Lord Vishnu. Lord Vishnu himself says this in Devi Bhagavatam.
Lord Vishnu had three wives, Ganga, Lakshmi and Saraswati. Saraswati felt that Sri Hari was partial to Lakshmi and Ganga and cursed others to born as tree and rivers . Ganga inturn cursed Saraswati to born as Rivers. Lord Vishnu placatetd them by saying that they would return His abode after purifying people of Bhooloka. He also said to Ganga that He would born as Shantanu and marry Ganga.
O Gange! You will also have to take incarnation in Bhârata as a river, purifying all the worlds, to destroy the sins of
the inhabitants of Bhârata. Bhagiratha will take you there after much entreating and worshipping you; and you will be famous by the name Bhagirathî, the most sanctifying river in the world. There, the Ocean born of my parts, and the King S'ântanu also born of my parts will be your husbands. O Bharatî! Let you go also and incarnate in part in Bhârata under the curse of Gangâ. O Good-natured One! Now go in full Amsas to Brahmâ and become His wife. Let Gangâ go also in Her fullness to S'iva. Let Padmâ remain with Me. Padmâ is of a peaceful nature, void of anger, devoted to Me and of a Sâttvika nature.
It is also mentioned in Mahabharata, Adi Parva, that Shantanu is not an ordinary person. He is very virtuous and of great energy.
Those old men that were touched by this monarch not only felt an indescribable sensation of pleasure but also became restored to youth. Therefore, this monarch was called Santanu.
Some other qualities of Shantanu is mentioned in Mahabharata, Adi Parva.
The monarch Santanu, the most adored of the gods and royal sages, was known in all the worlds for his wisdom, virtues, and truthfulness (of speech). The qualities of self-control, liberality, forgiveness, intelligence, modesty, patience and superior energy ever dwelt in that bull among men, viz., Santanu, that great being endued with these accomplishments and conversant with both religion and profit, the monarch was at once the protector of the Bharata race and all human beings. His neck was marked with (three) lines, like a conch-shell; his shoulders were broad, and he resembled in prowess an infuriated elephant. It would seem that all the auspicious signs of royalty dwelt in his person, considering that to be their fittest abode. Men, seeing the behaviour of that monarch of great achievements came to know that virtue was ever superior to pleasure and profit. These were the attributes that dwelt in that great being--that bull among men--Santanu. And truly there was never a king like Santanu.
When Bhishma has helped his father (Shantanu) in marrying Satyavati, he became very pleased with him and granted the boon of death at will (Ichhamrityu) as described in Mahabharata, Adi Parva.
And Santanu also, hearing of the extraordinary achievements of his son, became highly gratified and bestowed upon the high-souled prince the boon of death at will, saying, 'Death shall never come to thee as long as thou desirest to live. Truly death shall approach thee, O sinless one, having first obtained thy command.'"
And in Mahabhara, Bhishma Parva when Arjuna has pierced Bhishma with arrows by the help of Shikhandi, Bhishma himself admits it that now its time to fulfill his fathers boon of death at will.
Thus cut off by the angry Arjuna, that dart then fell down like a flash of lightning separated from a mass of clouds. Beholding his dart cut off, Bhishma became filled with rage. That hero, that subjugator of hostile cities, then began to reflect. And he said unto himself, 'With only a single bow I could slay all the Pandavas, if the mighty Vishnu himself had not been their protector. For two reasons, however, I will not fight with the Pandavas, viz., their unslayableness, and the femininity of Sikhandin. Formerly, when my sire wedded Kali, he pleased (with me) gave me two boons, viz., that I should be incapable of being slain in battle, and that my death should depend on my own choice. I should, however, now wish my own death, this being the proper hour.'
The boon that was granted to me by my illustrious sire, to the effect that my death would depend on my own wish O, let that boon become true. I will hold my life, since I have control in the matter of laying it down.' Having said these words to those swans, he continued to lie down on his bed of arrows.