Age-related cognitive decline associations with human electroencephalography (EEG) have previously focused on periodic activity. However, EEG is primarily made up of non-oscillatory aperiodic activity, which can be characterized with an exponent and offset value. In a secondary analysis of a cohort of 111 healthy participants aged 17-71 years, we examined the associations of the aperiodic exponent and offset with a battery of cognitive tests consisting of the Colour-Word Interference Test, Wechsler Adult Intelligence Scale IV Digit Span Test, Rey Auditory Learning Test, Delis-Kaplan Executive Function System Trial Making Test, and the Verbal Fluency Test. Using Principal Component Analysis and K-Means Clustering, we identified clusters of electrodes that exhibited similar aperiodic exponent and offset activity during resting-state eyes-closed EEG. Robust linear models were then used to model how aperiodic activity interacted with age and their associations with performance during each cognitive test. Offset by age interactions were identified for the Verbal Fluency Test, where smaller offsets were associated with poorer performance in adults as early as 33 years of age. Greater aperiodic activity is increasingly related to better verbal fluency performance with age in adulthood.