Smart city advancements are driving massive transformations of healthcare, the largest global industry. The drivers include increasing demands for ubiquitous, preventive, and personalized healthcare, to be provided to the public at reduced risks and costs. Mobile cloud computing could potentially meet the future healthcare demands by enabling anytime, anywhere capture and analyses of patients’ data. However, network latency, bandwidth, and reliability are among the many challenges hindering the realization of next-generation healthcare. This paper proposes a ubiquitous healthcare framework, UbeHealth, that leverages edge computing, deep learning, big data, high-performance computing (HPC), and the Internet of Things (IoT) to address the aforementioned challenges. The framework enables an enhanced network quality of service using its three main components and four layers. Deep learning, big data, and HPC are used to predict network traffic, which in turn are used by the Cloudlet and network layers to optimize data rates, data caching, and routing decisions. Application protocols of the traffic flows are classified, enabling the network layer to meet applications’ communication requirements better and to detect malicious traffic and anomalous data. Clustering is used to identify the different kinds of data originating from the same application protocols. A proof of concept UbeHealth system has been developed based on the framework. A detailed literature review is used to capture the design requirements for the proposed system. The system is described in detail including the algorithmic implementation of the three components and four layers. Three widely used data sets are used to evaluate the UbeHealth system.