We report measurements of branching fractions and time-dependent CP asymmetries in \(B^{0} \to D^{+}D^{-}\) and \(B^{0} \to D^{*\pm}D^{\mp}\) decays using a data sample that contains \((772 \pm 11)\times 10^6 B\bar{B}\) pairs collected at the \(\Upsilon(4S)\) resonance with the Belle detector at the KEKB asymmetric-energy \(e^+ e^-\) collider. We determine the branching fractions to be \(\mathcal{B}(B^{0} \to D^{+}D^{-})=(2.12 \pm 0.16 \pm 0.18)\times 10^{-4}\) and \(\mathcal{B}(B^{0} \to D^{*\pm}D^{\mp}=(6.14 \pm 0.29 \pm 0.50)\times 10^{-4}\). We measure CP asymmetry parameters \(\mathcal{S}_{D^{+}D^{-}} = -1.06_{-0.14}^{+0.21} \pm 0.08\) and \(\mathcal{C}_{D^{+}D^{-}} = -0.43 \pm 0.16 \pm 0.05\) in \(B^{0} \to D^{+}D^{-}\) and \(\mathcal{A}_{D^{*}D} = +0.06 \pm 0.05 \pm 0.02\), \(\mathcal{S}_{D^{*}D} = -0.78 \pm 0.15 \pm 0.05\), \(\mathcal{C}_{D^{*}D} = -0.01 \pm 0.11 \pm 0.04\), \(\Delta\mathcal{S}_{D^{*}D} = -0.13 \pm 0.15 \pm 0.04\) and \(\Delta\mathcal{C}_{D^{*}D} = +0.12 \pm 0.11 \pm 0.03\) in \(B^{0} \to D^{*\pm}D^{\mp}\), where the first uncertainty is statistical and the second is systematic. We exclude the conservation of CP symmetry in both decays at equal to or greater than \(4\sigma\) significance.