You can use gdal_translate utility. Use the option -scale [src_min src_max [dst_min dst_max]] with src_min and src_max as current min/max values from your data and 0,255 as dst_min,dst_max. Without the square brackets.
If you have installed QGIS with OSGeo4W package, you may have the terminal program called 'MSYS'. Open that and just use the gdal_translate command. If not, from within QGIS choose Raster -> Conversion - > Translate. Choose your files and options. At the bottom of the window the full gdal_translate command will be displayed. Click edit and add the -scale option.