This study demonstrates that GuruAgents, prompt-guided AI agents, can systematically operationalize the strategies of legendary investment gurus. We develop five distinct GuruAgents, each designed to emulate an iconic investor, by encoding their distinct philosophies into LLM prompts that integrate financial tools and a deterministic reasoning pipeline. In a backtest on NASDAQ-100 constituents from Q4 2023 to Q2 2025, the GuruAgents exhibit unique behaviors driven by their prompted personas. The Buffett GuruAgent achieves the highest performance, delivering a 42.2\% CAGR that significantly outperforms benchmarks, while other agents show varied results. These findings confirm that prompt engineering can successfully translate the qualitative philosophies of investment gurus into reproducible, quantitative strategies, highlighting a novel direction for automated systematic investing. The source code and data are available at https://github.com/yejining99/GuruAgents.