How to change the DPI of an image
Drop the image into the converter above, choose 300 DPI (or 72, 150, 600 or any value) and click download. The new file keeps its name with the DPI added, for example photo-300dpi.jpg.
In Photoshop the same setting lives under Image → Image Size with Resample switched off; on a Mac, Preview's Tools → Adjust Size does it with Resample image unchecked.