This paper addresses the problem of optimally covering a domain when the scalar function that describes the relative importance of the points in the domain is initially unknown. We propose an adaptive strategy for a team of cooperative robots that combines estimation and learning methods with optimal spatial coverage. The proposed algorithm leads the team of robots to an optimal solution of the coverage problem by efficiently trading off movement choices for learning the field with movement choices for covering the estimated field. The algorithm exploits the flexibility of Gaussian processes for learning the field and optimization rules based on Voronoi partitions of the environment for covering the field. We propose an exploration strategy that uses the decentralized nature of the coverage problem by allowing each robot to sample the space in its area of dominance. We provide a theoretical guarantee of the algorithm. The performance of the proposed algorithm is evaluated in simulation as well as on a team of mobile robots.