This paper develops an optimal acceleration/speed profile for a single autonomous vehicle crossing multiple signalized intersections without stopping in free flow mode. The design objective is to produce both time and energy efficient acceleration profiles of autonomous vehicles based on vehicle to infrastructure communication. Our design approach differs from most existing approaches based on numerical calculations: it begins with identifying the structure of the optimal acceleration profile and then showing that it is characterized by several parameters, which are used for design optimization. Therefore, the infinite dimensional optimal control problem is transformed into a finite dimensional parametric optimization problem, which enables a real-time online analytical solution. The simulation results show quantitatively the advantages of considering multiple intersections jointly rather than dealing with them individually. Based on mild assumptions, the optimal eco-driving algorithm is readily extended to include interfering traffic.