He has added that their surname will not protect them from the difficulties they might face because they are girls.
The 73-year-old star also advised them to not live "in the shadows of people's judgement" supported by their own wisdom.
The Bollywood megastar also posted a video of him reading the letter aloud.
On Teachers' Day on Monday, the "Paa" star penned an open letter to his grand-daughters, telling them it is a difficult world for women, and hoping that they will change things for good.
The letter read: "My very dearest Navya and Aaradhya, you both carry a very valuable legacy on your tender shoulders -- Aaradhya, the legacy of your par dada ji (great grandfather), Dr Harivansh Rai Bachchan...and Navya, the legacy of your par dada ji, Shri H.P. Nanda.
"Both your par dada ji gave your present surnames celebrated fame, dignity and recognition! Both of you maybe a Nanda or a Bachchan, but you are also girls...women! And because you are women, people will force their thinking, their boundaries on you."
Navya Naveli is the daughter of Amitabh's daughter Shweta Nanda, who also has a son named Agastya. And Aaradhya is Abhishek and Aishwarya Rai's daughter.
The cine icon also shared that it will be his honour to be known not as "Amitabh Bachchan, but as your grandfather".
The letter reads: "They will tell you how to dress, how to behave, who you can meet and where you can go. Don't live in the shadows of people's judgement. Make your own choices in the light of your own wisdom. Don't let anyone make you believe that the length of your skirt is a measure of your character."
"Don't let anyone's opinion of who you should be friends with, dictate who you will be friends with. Don't get married for any other reason other than you want to get married. People will talk. They shall say some terrible things. But that doesn't mean you have to listen to everyone. Never ever worry about -- log kya kahenge (what will people say)."
"At the end of the day, you are the only one who will face the consequences of your actions, so don't let other people make your decisions for you. Navya -- the privilege your name, your surname offers you, will not protect you from the difficulties you will face because you're a woman."
He wrote to four-year-old Aaradhya that "by the time you see and understand this, I may well not be around. But I think what I am saying today shall still be relevant. This may be a difficult, difficult world to be a woman. But I believe that it is women like you that will change that".
"It may not be easy, setting your own boundaries, making your own choices, rising above people's judgement. But you can set an example for women everywhere. Do this and you would have done more than I have ever done, and it will be my honour to be known not as Amitabh Bachchan, but as your grandfather!"