Large pre-trained models such as CLIP offer consistent accuracy across a range of data distributions when performing zero-shot inference (i.e., without fine-tuning on a specific dataset). Although existing fine-tuning approaches substantially improve accuracy in-distribution, they also reduce out-of-distribution robustness. We address this tension by introducing a simple and effective method for improving robustness: ensembling the weights of the zero-shot and fine-tuned models (WiSE-FT). Compared to standard fine-tuning, WiSE-FT provides large accuracy improvements out-of-distribution, while matching or improving in-distribution accuracy. On ImageNet (in-distribution) and five derived distribution shifts, WiSE-FT improves out-of-distribution accuracy by 2 to 10 percentage points (pp) while increasing in-distribution accuracy by nearly 1 pp relative to standard fine-tuning. WiSE-FT achieves similarly large robustness improvements (2 to 15 pp) on a diverse set of six further distribution shifts, and in-distribution accuracy gains of 0.8 to 3.3 pp compared to standard fine-tuning on seven commonly used transfer learning datasets. These improvements come at no additional computational cost during fine-tuning or inference.