Alzheimer's disease (AD) is a major neurodegenerative disease, and currently the leading cause of dementia in the world. The application of machine learning algorithms has recently brought a novel perspective to the early identification of neurological diseases such as AD, as they can advantageously exploit multivariate information in high-dimensional data to predict patient diagnosis and ultimately prognosis at the individual level. This work aimed to develop an early functional marker for AD using task-based and resting-state (RS) functional magnetic resonance imaging (fMRI), and to build a multimodal marker for predicting future conversion to AD. We found several regions of interest in which memory task-related fMRI activity could reliably discriminate between elderly controls and patients with prodromal AD, as well as functional connectivity during RS in the whole brain and within networks. Finally, we found that imaging markers were able to accurately predict conversion to AD, while clinical data was less informative.