Let H(B) denote the space of all holomorphic functions on the unit ball B of $mathbb{C}^n$. Let $varphi$ = (${varphi}_1,{ldots}{varphi}_n$) be a holomorphic self-map of B and $g{in}2$(B) with g(0) = 0. In this paper we study the boundedness and compactness of the generalized composition operator $C_{varphi}^gf(z)=int_{0}^{1}{mathfrak{R}}f(varphi(tz))g(tz){frac{dt}{t}}$ from generalized weighted Bergman spaces into Bloch type spaces.