Aggregation of amyloid-β (Aβ) peptide, a 39- to 43-residue fragment of the amyloid precursor protein, is associated with Alzheimer's disease, the most common form of dementia in the elderly population. Several experimental studies have tried to characterize the atomic details of amyloid fibrils, which are the final product of Aβ aggregation. Much less is known about species forming during the early stages of aggregation, in particular about the monomeric state of the Aβ peptide that may be viewed as the product of the very first step in the hypothesized amyloid cascade. Here, the equilibrium ensembles of monomeric Aβ alloforms Aβ(1-40) and Aβ(1-42) are investigated by Monte Carlo simulations using an atomistic force field and implicit solvent model that have been shown previously to correctly reproduce the ensemble properties of other intrinsically disordered polypeptides. Our simulation results indicate that at physiological temperatures, both alloforms of Aβ assume a largely collapsed globular structure. Conformations feature a fluid hydrophobic core formed, on average, by contacts both within and between the two segments comprising residues 12-21 and 24-40/42, respectively. Furthermore, the 11 N-terminal residues are completely unstructured, and all charged side chains, in particular those of Glu22 and Asp23, remain exposed to solvent. Taken together, these observations indicate a micelle-like† architecture at the monomer level whose implications for oligomerization, as well as fibril formation and elongation, are discussed. We establish quantitatively the intrinsic disorder of Aβ and find the propensity to form regular secondary structure to be low but sequence specific. In the presence of a global and unspecific bias for backbone conformations to populate the β-basin, the β-sheet propensity along the sequence is consistent with the arrangement of the monomer within the fibril, as derived from solid-state NMR data. These observations indicate that the primary sequence partially encodes fibril structure, but that fibril elongation must be thought of as a templated assembly step.