  We extend the theoretical prediction for the width difference $\Delta
\Gamma_q$ in the mixing of neutral $B$ mesons in the Standard Model to
next-to-next-to-leading order in $\alpha_s$. To this aim we calculate
three-loop diagrams with two $|\Delta B|=1$ current-current operators
analytically. In the matching between $|\Delta B|=1$ and $|\Delta B|=2$
effective theories we regularize the infrared divergences dimensionally and
take into account all relevant evanescent operators. Further elements of the
calculation are the two-loop renormalization matrix $Z_{ij}$ for the $|\Delta
B|=2$ operators and the $\mathcal{O}(\alpha_s^2)$ corrections to the finite
renormalization that ensures the $1/m_b$ suppression of the operator $R_0$ at
two-loop order. Our theoretical prediction reads $\Delta\Gamma_s/\Delta M_s =
{(4.33\pm 0.93)\cdot 10^{-3}}$ if expressed in terms of the bottom mass in the
$\overline{\rm MS}$ scheme and $\Delta\Gamma_s/\Delta M_s = {(4.20\pm
0.95)\cdot 10^{-3}}$ for the use of the potential-subtracted mass. While the
controversy on $|V_{cb}|$ affects both $\Delta\Gamma_s$ and $\Delta M_s$, the
ratio $\Delta\Gamma_s/\Delta M_s$ is not affected by the uncertainty in
$|V_{cb}|$ .
