Measures of intrinsic brain function at rest show promise as predictors of cognitive decline in humans, including EEG metrics such as individual α peak frequency (IAPF) and the aperiodic exponent, reflecting the strongest frequency of α oscillations and the relative balance of excitatory/inhibitory neural activity, respectively. Both IAPF and the aperiodic exponent decrease with age and have been associated with worse executive function and working memory. However, few studies have jointly examined their associations with cognitive function, and none have examined their association with longitudinal cognitive decline rather than cross-sectional impairment. In a preregistered secondary analysis of data from the longitudinal Midlife in the United States (MIDUS) study, we tested whether IAPF and aperiodic exponent measured at rest predict cognitive function (N = 235; age at EEG recording M = 55.10, SD = 10.71) over 10 years. The IAPF and the aperiodic exponent interacted to predict decline in overall cognitive ability, even after controlling for age, sex, education, and lag between data collection time points. Post hoc tests showed that “mismatched” IAPF and aperiodic exponents (e.g., higher exponent with lower IAPF) predicted greater cognitive decline compared to “matching” IAPF and aperiodic exponents (e.g., higher exponent with higher IAPF; lower IAPF with lower aperiodic exponent). These effects were largely driven by measures of executive function. Our findings provide the first evidence that IAPF and the aperiodic exponent are joint predictors of cognitive decline from midlife into old age and thus may offer a useful clinical tool for predicting cognitive risk in aging.