Principal $G$-bundles as pull back bundles.

Question

Let $G$ be a compact Lie group and consider a $G$-universal bundle $\pi: EG \to BG $ where $BG$ is the classifying space for the group $G$ and the bundle $\pi: EG \to BG $ is defined as the principal $G$-bundle such that $EG$ is a contractible space equipped with a free $G$-action and $BG:=EG / G$. Now let $X$ be a topological space. How can I prove that every principal $G$-bundle $\xi=(E,p,X)$ with base-space $X$ can be realized as the pull-back of the universal bundle $\pi: EG \to BG $?