The most recent results on mixing and $CP$ violation in the $B^0$ and $B_s^0$ systems published by the ATLAS experiment at the LHC are presented. The measurement of the $B_s^0 \to J/\psi \phi$ decay parameters, using data collected in $p p$ collisions at $\sqrt{s} = 7$ TeV and $\sqrt{s} = 8$ TeV and corresponding to 4.9 fb$^{-1}$ and 14.3 fb$^{-1}$ of integrated luminosity, includes the $CP$-violating phase $\phi_s$ and the width difference of the mass eigenstates $\Delta\Gamma_s$. The combined Run-1 results are $\phi_s = -0.098 \pm 0.084 \mbox{(stat.)} \pm 0.040 \mbox{(syst.)}$ rad and $\Delta\Gamma_s = 0.083 \pm 0.011 \mbox{(stat.)} \pm 0.007 \mbox{(syst.)} ~\mbox{ps}^{-1}$. The measured values agree with the Standard Model predictions. The second result presented is the measurement of the relative width difference $\Delta \Gamma_d / \Gamma_d$ of the $B^0$--$\bar B^0$ system, using data collected in $p p$ collisions at $\sqrt{s} = 7$ TeV and $\sqrt{s} = 8$ TeV, and corresponding to a total integrated luminosity of 25.2 fb$^{-1}$. The measured value is $\Delta \Gamma_d / \Gamma_d = (-0.1 \pm 1.1~\mbox{(stat.)} \pm 0.9~\mbox{(syst.)}) \times 10^{-2}$. Currently, this is the most precise single measurement of $\Delta \Gamma_d / \Gamma_d$. It agrees with the Standard Model prediction and measurements by other experiments.