In this paper, we introduce a novel framework for WEakly supervised Learning of Deep cOnvolutional neu-ral Networks (WELDON). Our method is dedicated to automatically selecting relevant image regions from weak annotations , e.g. global image labels, and encompasses the following contributions. Firstly, WELDON leverages recent improvements on the Multiple Instance Learning paradigm, i.e. negative evidence scoring and top instance selection. Secondly, the deep CNN is trained to optimize Average Precision , and fine-tuned on the target dataset with efficient computations due to convolutional feature sharing. A thorough experimental validation shows that WELDON outper-forms state-of-the-art results on six different datasets.