Distributed reinforcement learning algorithms for collaborative multi-agent Markov decision processes (MDPs) are presented and analyzed. The networked setup consists of a collection of agents (learners) which respond differently (depending on their instantaneous one-stage random costs) to a global controlled state and the control actions of a remote controller. With the objective of jointly learning the optimal stationary control policy (in the absence of global state transition and local agent cost statistics) that minimizes network-averaged infinite horizon discounted cost, the paper presents distributed variants of Q-learning of the consensus + innovations type in which each agent sequentially refines its learning parameters by locally processing its instantaneous payoff data and the information received from neighboring agents. Under broad conditions on the multi-agent decision model and mean connectivity of the inter-agent communication network, the proposed distributed algorithms are shown to achieve optimal learning asymptotically, i.e., almost surely (a.s.) each network agent is shown to learn the value function and the optimal stationary control policy of the collaborative MDP asymptotically. Further, convergence rate estimates for the proposed class of distributed learning algorithms are obtained.