The contribution of motor efficiency to the maintenance of psychological well-being in cognitively impaired older individuals is still insufficiently examined. This investigation primarily intended to evaluate whether muscular strength mediates the relationship between different facets of psychological well-being (i.e., personal satisfaction, emotional competence, coping), negative mood, and central executive efficiency through the Clock-Drawing, Trail-Making (Part A), and verbal fluency tests. Furthermore, the impact of cognitive decline on self-reported psychological well-being and depression was explored, using the handgrip strength (HGS) measure as a covariate. One hundred and nineteen older participants, 44 males and 75 females, aged 63 years and older (Mage = 77.7 years, SD = 5.6 years), completed a battery of tests assessing executive functions, HGS, depression, and psychological well-being. Significant low to moderate associations were found between distinct executive functions, HGS, psychological well-being, and depression. In addition, personal satisfaction did not correlate with any measure of executive functions, the clock-drawing score was associated only with coping index, and self-reported depression correlated only with the Trail-Making Test score. Moreover, a series of mediation analyses documented that executive functions (primarily assessing verbal fluency and motor speed) and HGS explained approximately 20–46% of the variance in perceived psychological well-being and depression. Finally, more cognitively impaired participants reported worse total psychological well-being, emotional competence, and coping. In conclusion, motor proficiency mediates the relationship between selective measures of executive functions and perceived psychological well-being and depression in cognitively impaired individuals.