In this paper, the fundamental problem of distribution and proactive caching of computing tasks in fog networks is studied under latency and reliability constraints. In the proposed scenario, computing can be executed either locally at the user device or offloaded to an edge cloudlet. Moreover, cloudlets exploit both their computing and storage capabilities by proactively caching popular task computation results to minimize computing latency. To this end, a clustering method to group spatially proximate user devices with mutual task popularity interests and their serving cloudlets is proposed. Then, cloudlets can proactively cache the popular tasks' computations of their cluster members to minimize computing latency. Additionally, the problem of distributing tasks to cloudlets is formulated as a matching game in which a cost function of computing delay is minimized under latency and reliability constraints. Simulation results show that the proposed scheme guarantees reliable computations with bounded latency and achieves up to 91% decrease in computing latency as compared to baseline schemes.