Background: Similar to most chronic diseases, Alzheimer's disease (AD) develops slowly from a preclinical phase into a fully expressed clinical syndrome. We aimed to use longitudinal data to calculate the rates of amyloid β (Aβ) deposition, cerebral atrophy, and cognitive decline. Methods: In this prospective cohort study, healthy controls, patients with mild cognitive impairment (MCI), and patients with AD were assessed at enrolment and every 18 months. At every visit, participants underwent neuropsychological examination, MRI, and a carbon-11-labelled Pittsburgh compound B (11C-PiB) PET scan. We included participants with three or more 11C-PiB PET follow-up assessments. Aβ burden was expressed as 11C-PiB standardised uptake value ratio (SUVR) with the cerebellar cortex as reference region. An SUVR of 1·5 was used to discriminate high from low Aβ burdens. The slope of the regression plots over 3-5 years was used to estimate rates of change for Aβ deposition, MRI volumetrics, and cognition. We included those participants with a positive rate of Aβ deposition to calculate the trajectory of each variable over time. Findings: 200 participants (145 healthy controls, 36 participants with MCI, and 19 participants with AD) were assessed at enrolment and every 18 months for a mean follow-up of 3·8 (95% CI CI 3·6-3·9) years. At baseline, significantly higher Aβ burdens were noted in patients with AD (2·27, SD 0·43) and those with MCI (1·94, 0·64) than in healthy controls (1·38, 0·39). At follow-up, 163 (82%) of the 200 participants showed positive rates of Aβ accumulation. Aβ deposition was estimated to take 19·2 (95% CI 16·8-22·5) years in an almost linear fashion-with a mean increase of 0·043 (95% CI 0·037-0·049) SUVR per year-to go from the threshold of 11C-PiB positivity (1·5 SUVR) to the levels observed in AD. It was estimated to take 12·0 (95% CI 10·1-14·9) years from the levels observed in healthy controls with low Aβ deposition (1·2 [SD 0·1] SUVR) to the threshold of 11C-PiB positivity. As AD progressed, the rate of Aβ deposition slowed towards a plateau. Our projections suggest a prolonged preclinical phase of AD in which Aβ deposition reaches our threshold of positivity at 17·0 (95% CI 14·9-19·9) years, hippocampal atrophy at 4·2 (3·6-5·1) years, and memory impairment at 3·3 (2·5-4·5) years before the onset of dementia (clinical dementia rating score 1). Interpretation: Aβ deposition is slow and protracted, likely to extend for more than two decades. Such predictions of the rate of preclinical changes and the onset of the clinical phase of AD will facilitate the design and timing of therapeutic interventions aimed at modifying the course of this illness. Funding: Science and Industry Endowment Fund (Australia), The Commonwealth Scientific and Industrial Research Organisation (Australia), The National Health and Medical Research Council of Australia Program and Project Grants, the Austin Hospital Medical Research Foundation, Victorian State Government, The Alzheimer's Drug Discovery Foundation, and the Alzheimer's Association.