Monolayers (MLs) of semiconducting transition metal dichalcogenides (S-TMDs), e.g. MoSe2 and WSe2, are direct bandgap semiconductors characterized by very interesting optical and electronic properties. S-TMD alloys have emerged as materials with tunable electronic structures and valley polarizations. In this work, we investigate magneto-optical properties of excitonic complexes in MoxW1-xSe2 ML encapsulated in hexagonal BN (hBN) with different ratios of Mo and W atoms. Under applied magnetic fields, the neutral exciton resonances in S-TMD MLs split into two circularly polarized components as a result of the Zeeman effect. Using low-temperature photoluminescence (PL) experiments carried out in external out-of-plane magnetic fields up to 30 T, we extract the g-factors of the neutral (X) and charged (T) excitons. The g-factors for the X transitions change gradually from about -4 up to about -10. This striking tunability is verified by first-principles calculations of the band structures. The calculated values of the g-factors show a trend similar to the experimental ones, and also reveal an additional increase and decrease under application of the compressive or tensile biaxial strains, respectively. Alloying of S-TMD MLs is an efficient mechanism to enhance the g-factors of neutral excitons, up to values that have only been observed for interlayer excitons in TMDs heterostructures. Due to the much simpler fabrication process of MLs compared to TMD HSs with specific twist angles, alloy MLs open new avenues as potential candidates for valleytronic and quantum devices.