In this study, we define the double Ces\`aro sequence spaces $\operatorname{Ces}_p$, $\operatorname{Ces}_{bp}$ and $\operatorname{Ces}_{bp0}$ and examine some properties of those sequence spaces. Furthermore, we determine the $\beta(bp)$-duals of the spaces $\operatorname{Ces}_{bp}$ and $\operatorname{Ces}_p$.