Time series data is ubiquitous across various domains, including manufacturing, finance, and healthcare. High-quality annotations are essential for effectively understanding time series and facilitating downstream tasks; however, obtaining such annotations is challenging, particularly in mission-critical domains. In this paper, we propose TESSA, a multi-agent system designed to automatically generate both general and domain-specific annotations for time series data. TESSA introduces two agents: a general annotation agent and a domain-specific annotation agent. The general agent captures common patterns and knowledge across multiple source domains, leveraging both time-series-wise and text-wise features to generate general annotations. Meanwhile, the domain-specific agent utilizes limited annotations from the target domain to learn domain-specific terminology and generate targeted annotations. Extensive experiments on multiple synthetic and real-world datasets demonstrate that TESSA effectively generates high-quality annotations, outperforming existing methods.