Efficient mobility is a key aspect for the future smart cities. The real added value for smart cities is the real-time optimization of vehicular and public transportation flows to reduce traffic congestions, costs, and emissions. Observing constantly the behaviour of people moving around the city can help policy makers to act promptly and to fix congested flows dynamically. In this paper, we describe from a technical point-of-view an original use of big data (coming from the cellular network of the Vodafone Italy Telco operator) to compute mobility patterns for smart cities. The paper also discusses five innovative mobility patterns that describe different mobility scenarios of the city, starting from how people move around point-of-interests of the city in real time. The mobility patterns have been experimentally validated in a real industrial setting and for the Milan metropolitan city. The study conducted confirmed the quality of the patterns and their importance in smart cities, by showing how cell phone big data can complete other sources of people information. These mobility patterns can be exploited by policy makers to improve the mobility in a city, or by Navigation Systems and Journey Planners to provide final users with accurate travel plans.