The singer and his husband David Furnish became parents to baby Zachary Jackson Levon through a surrogate mother on Christmas Day.
He told Saga: "I so value my own childhood now, and the sense of wonder and personal discovery that I enjoyed, that we want to give Zachary - as much as we possibly can - the same thing. A solid old-fashioned childhood, if you like.
"I know it'll be hard with my life, but we want him to have that same normality and for things in life to have real value. So we don't intend to spoil him - we're going to try to give him a fun, carefree time of innocence, freedom, love and stability."
The 63-year-old explained that he doesn't think children appreciate things in the same way that he did as a youngster.
He added: "I don't know if kids get that sort of enjoyment out of things anymore. I don't think you can do because your parents worked so hard when money was scarce to buy you a bicycle or your first record player.
"I don't want to become Britain's crustiest old man but I don't think you can possibly have the pleasure now of growing up like we did. A trip to the cinema was a treat, a trip up to London was unbelievably exciting. A trip anywhere."