Caching popular videos at the edge has been confirmed as a promising way to support low-latency video transmission and alleviate the backhaul traffic burden. Meanwhile, mobile edge computing (MEC) has also been regarded as an effective solution to meet the 5G low-latency service requirements. In this paper, we propose to fully utilize both the storage and computing resources at edge servers to support multiple bitrate video streaming. We design the video caching, processing, and user association models that aim to minimize the average retrieval latency of all users. This problem is modeled as a mixed-integer bilinear problem, which is NP-hard. We show that under practical constraints on storage, bandwidth, and processing capacity, the problem does not exhibit sub-modular property and the performance of a greedy algorithm may not be strictly guaranteed. To deal with this challenging problem, we decompose the original problem into a cache placement problem and a user-BS association problem, while still preserving the interplay between the two sub-problems. A linearization and rounding algorithm, including: (i) a greedy rounding proactively caching scheme and (ii) a random-rounding user-BS association scheme, is then proposed, with performance bounds derived. Extensive simulation results show that the proposed scheme can achieve a near-optimal performance under various storage, computing capacity, and downlink bandwidth settings.Index Terms-Video caching, video transcoding, multiple bitrate video, mobile edge computing (MEC), submodularity.