Khan, who worked with the legendary star in Kabhie Khushi Kabhie Gham and Mohabattein, described Bachchan as 'magical' in the NDTV Movies video.
Recalling his childhood memories of meeting Bachchan, who turned 70 on Thursday (October 11), Khan said: "He used to come over to our house in Bangalore. We used to call him 'Lambhu Uncle'. He would always give us sweets.
"I don't know if he remembers this. Every time we rushed up he would give us these sweets. He was our morning supply of toffees and sweets. That's my first memory of Amitabh Bachchan."
Khan explained that he is a lifelong fan of the veteran actor having grown up watching all his films.
"That's the greatness of Mr Amitabh Bachchan. That you can describe your life span with Bachchan films. I remember in my childhood it was Bombay to Goa, then ten years later 'The Angry Young Man, Chal Mere Bhai' (Naseeb). 'I can talk English, I can walk English because English is a very funny language...' (Namak Halal). I know every moment, every scene, every gesture from his films.
"You have to see it from the point of view of a guy who has grown up wanting to be Amitabh Bachchan. There's your parents that teach you about life and your school that teaches you stuff, and then there's Mr Amitabh Bachchan, who you just want to be. I'm not saying I wanted to be an actor like him or a star like him. I just wanted to be Mr Amitabh Bachchan."
The 47-year-old actor, who starred in a remake of the 1978 classic Amitabh Bachchan film Don, said he would not deign to copy the superstar.
"Never in my career would I try to copy Mr Amitabh Bachhan, Mr Dilip Kimar, Hema Maliniji, Balraj Sahni saab, Mr.Yash Chopra, Naseeruddin Shah. You don't try to copy them. You don't try to do anything they've done. When you say a line of theirs or you mention their name, you are only saying it with respect and as [an] homage."
The Jab Tak Hain Jaan star said that Bachchan was akin to an acting institution.
"I would say this to someone that if you really want to [learn] but don't have a teacher or a theatre background, just start [with] his movies and see them all - up to [game show] KBC at 9pm in the evening. You'll learn all there is to know about acting."
Addressing Bachchan directly, he added: "I can say that on my behalf, because a lot of things I have learnt and love are because of you. That's the beauty of you. That you don't even know the lives that you touch and one of them is mine.
"God bless you on your 70th birthday and I really pray for your health that you live another 100 years so that my children and their children can be subjected to the experience, the magnificence the radiance, the greatness, the brilliance and the love of the one and only Mr Amitabh Bachchan."