We investigated whether amyloid-β (Aβ) and tau affected cognition in cognitively normal (CN) individuals, and whether norms for neuropsychological tests based on biomarker-negative individuals would improve early detection of dementia. We included 907 CN individuals from 8 European cohorts and from the Alzheimer's disease Neuroimaging Initiative. All individuals were aged above 40, had Aβ status and neuropsychological data available. Linear mixed models were used to assess the associations of Aβ and tau with five neuropsychological tests assessing memory (immediate and delayed recall of Auditory Verbal Learning Test, AVLT), verbal fluency (Verbal Fluency Test, VFT), attention and executive functioning (Trail Making Test, TMT, part A and B). All test except the VFT were associated with Aβ status and this influence was augmented by age. We found no influence of tau on any of the cognitive tests. For the AVLT Immediate and Delayed recall and the TMT part A and B, we calculated norms in individuals without Aβ pathology (Aβ- norms), which we validated in an independent memory-clinic cohort by comparing their predictive accuracy to published norms. For memory tests, the Aβ- norms rightfully identified an additional group of individuals at risk of dementia. For non-memory test we found no difference. We confirmed the relationship between Aβ and cognition in cognitively normal individuals. The Aβ- norms for memory tests in combination with published norms improve prognostic accuracy of dementia.