Monolayers (MLs) of semiconducting transition metal dichalcogenides emit light very efficiently and display rich spin-valley physics, with gyromagnetic (g) factors of about -4. Here, we investigate how these properties can be tailored by alloying. Magneto-optical spectroscopy is used to reveal the peculiar properties of excitonic complexes in Mo_{x}W_{1-x}Se_{2} MLs with different metal concentrations. We show that the alloys feature extremely high g factors for neutral excitons, that change gradually with the composition up to reaching values of the order of -10 for x≈0.2. First-principles calculations quantitatively identify the alloy-induced mixing between different conduction band valleys as the underlying mechanism originating the anomalous composition dependence of the neutral exciton g factor. The theoretical framework also suggests a high strain sensitivity of the alloys, making them promising candidates for tailor-made optoelectronic devices.