Artificial intelligence (AI) has taken us by storm, helping us to make decisions in everything we do, even in finding our “true love” and the “significant other”. While 5G promises us high-speed mobile internet, 6G pledges to support ubiquitous AI services through next-generation softwarization, heterogeneity, and configurability of networks. The work on 6G is in its infancy and requires the community to conceptualize and develop its design, implementation, deployment, and use cases. Towards this end, this paper proposes a framework for Distributed AI as a Service (DAIaaS) provisioning for Internet of Everything (IoE) and 6G environments. The AI service is “distributed” because the actual training and inference computations are divided into smaller, concurrent, computations suited to the level and capacity of resources available with cloud, fog, and edge layers. Multiple DAIaaS provisioning configurations for distributed training and inference are proposed to investigate the design choices and performance bottlenecks of DAIaaS. Specifically, we have developed three case studies (e.g., smart airport) with eight scenarios (e.g., federated learning) comprising nine applications and AI delivery models (smart surveillance, etc.) and 50 distinct sensor and software modules (e.g., object tracker). The evaluation of the case studies and the DAIaaS framework is reported in terms of end-to-end delay, network usage, energy consumption, and financial savings with recommendations to achieve higher performance. DAIaaS will facilitate standardization of distributed AI provisioning, allow developers to focus on the domain-specific details without worrying about distributed training and inference, and help systemize the mass-production of technologies for smarter environments.