  Using a combination of density functional theory and dynamical mean field
theory we show that electric polarization and magnetism are strongly
intertwined in (TMTTF)$_2$-$X$ (X$=$PF$_6$, As$F_6$, and SbF$_6$) organic
crystals and they originate from short-range Coulomb interactions. Electronic
correlations induce a charge-ordered state which, combined with the molecular
dimerization, gives rise to a finite electronic polarization and to a
ferroelectric state. We predict that the value of the electronic polarization
is enhanced by the onset of antiferromagnetism showing a sizable
magnetoelectric leading to a multiferroic behavior of (TMTTF)$_2$-$X$
compounds.
