We present free high quality multi-speaker speech corpora for Gujarati, Kannada, Malayalam, Marathi, Tamil and Telugu, which are six of the twenty two official languages of India spoken by 374 million native speakers. The datasets are primarily intended for use in text-to-speech (TTS) applications, such as constructing multilingual voices or being used for speaker or language adaptation. Most of the corpora (apart from Marathi, which is a female-only database) consist of at least 2,000 recorded lines from female and male native speakers of the language. We present the methodological details behind corpora acquisition, which can be scaled to acquiring data for other languages of interest. We describe the experiments in building a multilingual text-to-speech model that is constructed by combining our corpora. Our results indicate that using these corpora results in good quality voices, with Mean Opinion Scores (MOS) > 3.6, for all the languages tested. We believe that these resources, released with an open-source license, and the described methodology will help in the progress of speech applications for the languages described and aid corpora development for other, smaller, languages of India and beyond.