In the present article, we define the Mexican hat wavelet Stieltjes transform (MHWST) by applying the concept of Mexican hat wavelet transform [9]. The proposed transform serves as a centralized method to analyze both discrete and continuous time-frequency localization. Besides the formulation of all the fundamental results, a reconstruction formula is also obtained for MHWST. Further, a unified approach is applied to obtain the necessary and sufficient conditions for the same. Moreover, simplified construction for the jump operator is also presented for the Mexican hat wavelet Stieltjes transform.