This paper presents ExPECA, an edge computing and wireless communication research testbed designed to tackle two pressing challenges: comprehensive end-to-end experimentation and high levels of experimental reproducibility. Leveraging OpenStack-based Chameleon Infrastructure (CHI) framework for its proven flexibility and ease of operation, ExPECA is located in a unique, isolated underground facility, providing a highly controlled setting for wireless experiments. The testbed is engineered to facilitate integrated studies of both communication and computation, offering a diverse array of Software-Defined Radios (SDR) and Commercial Off-The-Shelf (COTS) wireless and wired links, as well as containerized computational environments. We exemplify the experimental possibilities of the testbed using OpenRTiST, a latency-sensitive, bandwidthintensive application, and analyze its performance. Lastly, we highlight an array of research domains and experimental setups that stand to gain from ExPECA's features, including closed-loop applications and time-sensitive networking.