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Reservoir Computing is a bio-inspired computing paradigm for processing time-dependent signals (Jaeger and Haas 2004; Maass, Natschläger, and Markram 2002). The performance of its hardware implementation (see e.g. (Soriano et al. 2015) for a review) is comparable to state-of-the-art digital algorithms on a series of benchmark tasks.The major bottleneck of these implementation is the readout layer, based on slow offline post-processing. Several analogue solutions have been proposed (Smerieri et al. 2012; Duport et al. 2016; Vinckier et al. 2016), but all suffered from noticeable decrease in performance due to added complexity of the setup. Here we propose the online learning approach to solve these issues. We present an experimental reservoir computer with a simple analogue readout layer, based on previous works, and show numerically that online learning allows to disregard the added complexity of an analogue layer and obtain the same level of performance as with a digital layer. This work thus demonstrates that online training allows building high-performance fully-analogue reservoir computers, and represents an important step towards experimental validation of the proposed solution.