The deep integration of mobile networks with artificial intelligence (AI) has emerged as a pivotal driving force for the sixth-generation (6G) mobile network. AI-native 6G represents a paradigm shift for mobile networks, as it not only embeds AI into network components to enhance network intelligence and automation but also transforms 6G into a foundational infrastructure for enabling pervasive AI applications and services. This paper proposes a novel 6G AI-native architecture. The challenges and requirements for the AI-native 6G mobile network are first analyzed, followed by the development of a task-driven approach for architecture design based on insights from system theory. Then, a 6G AI-native architecture is proposed, featuring the integration of distributed AI data and computing components with layered centralized collaborative control and flexible on-demand deployment. Key components and procedures for the 6G AI-native architecture are also discussed in detail. Finally, standardization practices for the convergence of mobile networks and AI in fifth-generation (5G) networks are analyzed, and an outlook on the standardization of AI-native design in 6G is given. This paper aims to provide not only theoretical insights into AI-native architecture design methodology but also a comprehensive 6G AI-native architecture that lays a foundation for the transition from mobile communications toward mobile information services in the 6G era.