Current exoskeleton designs have opened new ways to therapists and patients for muscle maintenance and strength recovery therapy approaches. However, some issues remain to be solved. Lack of adaptation, versatility, or overweight are some of the main factors that should be improved. In this article, we present a novel design for a functional modular exoskeleton composed of four independent active joints using a decentralized electronic architecture, being the first wearable exoskeleton to apply this technology. This new approach avoids the use of a main processor, and the modular scheme allows every possible configuration between the hip and knee. The decentralized electronic architecture is enabled by implementing adaptive central pattern generator (CPG) algorithms in each module controller. Each CPG has been trained to mimic the joint trajectory of a healthy person walking. The communication between modules assures their coordination through synchronization terms. The operation of each configuration was first tested on a bench at different speeds and later used by a healthy subject. These tests show how the decentralized control strategy maintains the synchronization between modules, reproducing and adapting the trained walking pattern. These results prove that our proposal is suitable for the development of exoskeletons focused on personalized therapies.