Perovskite-like compounds are widely known as model systems for studying the relationships between crystal structure and physical properties. Among them, magnetically-ordered ferroelectric oxides have attracted much attention in recent years. Such materials combine spin and electric dipole ordering in the same phase, thus providing the technologically important possibility to control magnetism with an electric field. While BiFeO3 is the most thoroughly studied magnetic ferroelectric compound, the properties of its solid solutions remain a matter of intensive debate. In this work we show how variation in the chemical composition of Bi1-xAExFe1-xTixO3 (AE= Ca, Sr, Ba; x≤0.2) perovskites affects their crystal structure and magnetic behavior. In particular, our research demonstrates that Ca/Ti and Sr/Ti substitutions suppress the cycloidal antiferromagnetic structure specific to the parent compound, thus stabilizing a weak ferromagnetic and ferroelectric state. The Ba/Ti-doped solid solutions retain the magnetic behavior characteristic of the pure BiFeO3. The composition-driven changes in the magnetic properties of the Bi1-xAExFe1-xTixO3 compounds correlate with the structural evolution, thus confirming the existence of a tight coupling between the magnetic and electric dipole order.