We obtain the jointly optimal power allocation and partner selection policies, that maximize the sum rate of a cooperative OFDMA system with mutually cooperating pairs of users. We show that the power allocation and partner selection steps can be performed sequentially, and the latter step can be formulated as a maximum weighted matching problem on an undirected graph, which can be solved in polynomial time. We further propose practical algorithms, and compare their performances to the optimal matching algorithm, and demonstrate that very simple and low complexity algorithms based on user-user and user-receiver distances may provide near-optimum rate performance. Moreover, we observe that algorithms that achieve superior sum-rate performance, surprisingly pair the cell edge users, with the strong users near the base station.