Nowadays in modern societies, a sedentary lifestyle is almost inevitable for a majority of the population. Long hours of sitting, especially in wrong postures, may result in health complications. A smart chair with the capability to identify sitting postures can help reduce health risks induced by a modern lifestyle. This paper presents the design, realization and evaluation of a new smart chair sensors system capable of sitting postures identification. The system consists of eight pressure sensors placed on the chair's sitting cushion and the backrest. A signal acquisition board was designed from scratch to acquire data generated by the pressure sensors and transmit them via a Wi-Fi network to a purposely developed graphical user interface which monitors and stores the acquired sensors' data on a computer. The designed system was tested by means of an extensive sitting experiment involving 40 subjects, and from the acquired data, the classification of the respective sitting postures out of eight possible postures was performed. Hereby, the performance of seven deep-learning algorithms was assessed. The best accuracy of 91.68% was achieved by an echo memory network model. The designed smart chair sensors system is simple and versatile, low cost and accurate, and it can easily be deployed in several smart chair environments, both for public and private contexts.