Nowadays, video coding and transcoding have a great interest and important impact in areas such as high-definition video and entertainment, healthcare and elderly care, high-resolution video surveillance, self-driving cars, or e-learning. This growing demand for high-resolution video boosts the proposal of new codecs and the development of their encoders that require high computational requirements. Therefore, new strategies are needed to accelerate them. Cloud infrastructures offer interesting features for video coding, such as on-demand resource allocation, multitenancy, elasticity, and resiliency. This paper proposes a cloud-based distributed architecture, where the network and the storage layers have been tuned, to accelerate video encoders over an elastic number of worker encoder nodes. Moreover, an application is developed and executed in the proposed architecture to allow the creation of encoding jobs, their dynamic assignment, their execution in the worker encoder nodes, and the reprogramming of the failed ones. To validate the proposed architecture, the parallel execution of existing video encoders, x265 for H.265/HEVC and libvpx-vp9 for VP9, has been evaluated in terms of scalability, workload, and job distribution, varying the number of encoder nodes. The quality of the encoded videos has been analyzed for different bit rates and number of frames per job using the Peak Signal-to-Noise Ratio (PSNR). Results show that our proposal maintains video quality compared with the sequential encoding while improving encoding time, which can decrease near 90%, depending on the codec and the number of encoder nodes.