Recently there has been a growing attention on the use of web and social data to improve traditional prediction models in politics, finance, marketing and health, but even though a correlation between observed phenomena and related social data has been demonstrated in many cases, yet the effectiveness of the latter for long-term or even mid-term predictions has not been shown. In epidemiological surveillance, the problem is compounded by the fact that infectious diseases models (such as susceptible-infected-recovered-susceptible, SIRS) are very sensitive to current conditions, such that small changes can produce remarkable differences in future outcomes. Unfortunately, current or nearly-current conditions keep changing as data are collected and updated by the epidemiological surveillance organizations. In this paper we show that the time series of Twitter messages reporting a combination of symptoms that match the influenza-like-illness (ILI) case definition represent a more stable and reliable information on "current conditions", to the point that they can replace, rather than simply integrate, official epidemiological data. We estimate the effectiveness of these data at predicting current and past flu seasons (17 seasons overall), in combination with official historical data on past seasons, obtaining an average correlation of 0.85 over a period of 17 weeks covering the flu season.