In this paper, the ambient temperature multiferroic effect resulting from the incorporation of transition metal ions (Fe3+ and Co2+) in lead-free BST[Ba0.7Sr0.3(Fex/2Cox/2)Ti1-xO3; x= 0, 0.01, 0.03, 0.05, 0.07] ceramics synthesized via the solid-state reaction (SSR) procedure has been thoroughly analyzed. The investigation consistently scrutinized the effects of augmenting transition metal co-doping on the structural, ferroelectric, dielectric, magnetic, and magnetodielectric characteristics. The X-ray diffraction (XRD) patterns for all ceramic compositions demonstrated the formation of a monophasic (P4mm) crystalline structure. The Raman analysis evidenced the presence of various modes, which are associated with the occurrence of the single-phase and provide strong corroboration for the X-ray diffraction observations. Scanning electron micrographs reveals that the inclusion of transition metal ions results in the diminution of grain size. The frequency-dependent dielectric characteristics were represented over the frequency range of 1 kHz to 1 MHz. The P-E hysteresis curves demonstrate a consistent reduction in the values of Ps and Pr, whereas, the M-H curve reveals the enhancement in magnetic properties with increased doping. The magnetodielectric analysis confirmed the interplay between the ferroelectric and ferromagnetic ordering. The BST-1CF sample exhibited the highest MC % value of 5.30 % along with the magnetoelectric coupling coefficient 'γ' of - 6.01×10^-1 (memu/g)^-2, making it a favorable entrant for the advancement of innovative non-volatile multiferroic memory gadgets.