  We reveal the microscopic origin of electric polarization $\vec{P}$ induced
by noncollinear magnetic order. We show that in Mott insulators, such $\vec{P}$
is given by all possible combinations of position operators $\hat{\vec{r}}_{ij}
= (\vec{r}_{ij}^{\, 0},\vec{\boldsymbol{r}}_{ij}^{\phantom{0}})$ and transfer
integrals $\hat{t}_{ij} = (t_{ij}^{0},\boldsymbol{t}_{ij}^{\phantom{0}})$ in
the bonds, where $\vec{r}_{ij}^{\, 0}$ and $t_{ij}^{0}$ are spin-independent
contributions in the basis of Kramers doublet states, while
$\vec{\boldsymbol{r}}_{ij}^{\phantom{0}}$ and
$\boldsymbol{t}_{ij}^{\phantom{0}}$ stem solely from the spin-orbit
interaction. Among them, the combination $t_{ij}^{0}
\vec{\boldsymbol{r}}_{ij}^{\phantom{0}}$, which couples to the spin current,
remains finite in the centrosymmetric bonds, thus yielding finite $\vec{P}$ in
the case of noncollinear arrangement of spins. The form of the magnetoelectric
coupling, which is controlled by $\vec{\boldsymbol{r}}_{ij}^{\phantom{0}}$,
appears to be rich and is not limited to the phenomenological law $\vec{P} \sim
\boldsymbol{\epsilon}_{ij} \times [\boldsymbol{e}_{i} \times
\boldsymbol{e}_{j}]$ with $\boldsymbol{\epsilon}_{ij}$ being the bond vector
connecting the spins $\boldsymbol{e}_{i}$ and $\boldsymbol{e}_{j}$. Using
density-functional theory, we illustrate how the proposed mechanism work in the
spiral magnets CuCl$_2$, CuBr$_2$, CuO, and $\alpha$-Li$_2$IrO$_3$, providing
consistent explanation to available experimental data.
