As well" means "equally well", not "too." In recent times people have confused its meaning. In proper English, the following two constructions have different shades of meaning:
"Jack speaks Russian. He speaks English, too." (Jack speaks both languages--"too" is additive).
"Jack speaks Russian. He speaks English as well." (Jack speaks them equally well--"as well" is comparativel).
The confusion probably started because of sentences such as "Your brother knows that's not allowed and you know as well." The "as well" is short for "as well as he does", but could be confused in its meaning for "too" or "also."
The distinction is being lost because broadcast schools teach their students to end sentences with "as well" to sound "professional", and impressionable listeners follow suit, especially in formal settings but more and more in casual speech.
So strictly speaking, "I have this book as well" is ungrammatical. One cannot "have a book well", and there is no basis of comparison. But you could say, "I authored this book, and wrote this one as well." If you want to avoid suggesting that you wrote the two books with equal skill, then you would end with "also" or "too".