Foundation models for weather science are pre-trained on vast amounts of structured numerical data and outperform traditional weather forecasting systems. However, these models lack language-based reasoning capabilities, limiting their utility in interactive scientific workflows. Large language models (LLMs) excel at understanding and generating text but cannot reason about high-dimensional meteorological datasets. We bridge this gap by building the first agentic framework for weather science. Our framework includes a Python code-based environment for agents (ZephyrusWorld) to interact with weather data, featuring tools including a WeatherBench 2 dataset indexer, geolocator for geocoding from natural language, weather forecasting, climate simulation capabilities, and a climatology module for querying precomputed climatological statistics (e.g., means, extremes, and quantiles) across multiple timescales. We design Zephyrus, a multi-turn LLM-based weather agent that iteratively analyzes weather datasets, observes results, and refines its approach through conversational feedback loops. We accompany the agent with a new benchmark, ZephyrusBench, with a scalable data generation pipeline that constructs diverse question-answer pairs across weather-related tasks, from basic lookups to advanced forecasting, extreme event detection, and counterfactual reasoning. Experiments on this benchmark demonstrate the strong performance of Zephyrus agents over text-only baselines, outperforming them by up to 44 percentage points in correctness. However, the hard tasks are still difficult even with frontier LLMs, highlighting the challenging nature of our benchmark and suggesting room for future development. Our codebase and benchmark are available at https://github.com/Rose-STL-Lab/Zephyrus.