To survive and thrive in complex environments, humans have evolved sophisticated self-improvement mechanisms through environment exploration, hierarchical abstraction of experiences into reuseable skills, and collaborative construction of an ever-growing skill repertoire. Despite recent advancements, autonomous web agents still lack crucial self-improvement capabilities, struggling with procedural knowledge abstraction, refining skills, and skill composition. In this work, we introduce SkillWeaver, a skill-centric framework enabling agents to self-improve by autonomously synthesizing reusable skills as APIs. Given a new website, the agent autonomously discovers skills, executes them for practice, and distills practice experiences into robust APIs. Iterative exploration continually expands a library of lightweight, plug-and-play APIs, significantly enhancing the agent’s capabilities. Experiments on WebArena and real-world websites demonstrate the efficacy of SkillWeaver, achieving relative success rate improvements of 31.8% and 39.8%, respectively. Additionally, APIs synthesized by strong agents substantially enhance weaker agents through transferable skills, yielding improvements of up to 54.3% on WebArena. These results demonstrate the effectiveness of honing diverse website interactions into APIs, which can be seamlessly shared among various web agents.