It has become a consensus that the integration of computing, sensing, and communication with ubiquitous intelligence will be the cornerstone of the sixth-generation (6G) network. The concept of edge computing and intelligence, which push the frontier of computation closer to the data source, is a suitable paradigm that aligns with these visions of 6G. In this article, we introduce Agent-as-a-Service (AaaS), an AI-native edge computing framework that leverages AI agents for both the control-plane operations and user-plane services of the 6G network. In the AaaS framework, agents can perform computing, sensing, and communicating tasks automatically by harnessing of the pervasive intelligence offered by 6G infrastructures. By AI-native, we refer to redesigning the whole lifecycle of an edge computing task to align with the prominent reasoning and planning ability of the generative AI. The lifecycle includes plan generation, execution orchestration, resource management, and long-term evolvement. The AaaS framework is built upon emerging techniques such as deviceless computing and WebAssembly to cope with the heterogeneous and geo-distributed 6G edge deployments. Based on the AaaS framework, we conduct a case study on autonomous driving in 6G edge computing to showcase the benefits in terms of overall latency reduction. Finally, we outline potential research directions to form a more efficient and integrated 6G edge computing with artificial intelligence.