Growing evidence about the link between cognitive and physical decline suggests the early changes in physical functioning as a potential biomarker for cognitive impairment. Thus, we compared grip-strength trajectories over 12–16 years in three groups classified according to their cognitive status (two stable patterns, normal and impaired cognitive performance, and a declining pattern) in two representative UK and Chilean older adult samples. The samples consisted of 7069 UK (ELSA) and 1363 Chilean participants (ALEXANDROS). Linear Mixed models were performed. Adjustments included socio-demographics and health variables. The Declined and Impaired group had significantly lower grip-strength at baseline when compared to the Non-Impaired. In ELSA, the Declined and Impaired showed a faster decline in their grip strength compared to the Non-Impaired group but differences disappeared in the fully adjusted models. In ALEXANDROS, the differences were only found between the Declined and Non-Impaired and they were partially attenuated by covariates. Our study provides robust evidence of the association between grip strength and cognitive performance and how socio-economic factors might be key to understanding this association and their variability across countries. This has implications for future epidemiological research, as hand-grip strength measurements have the potential to be used as an indicator of cognitive performance.