Files with .webhistory extension store history data of web browsing in Apple Safari browser. Safari on Mac OS X saves history information in these files by default in folder [user] / Library / Caches / Metadata / Safari / History.
The .webhistory file extension is related to Apple Safari and its history files. These files are not meant to directly open as they contain temporary caches and internal data.
The software recommended for managing .webhistory files is Safari web browser. Apple defined the .webhistory file format standard known as Safari Web History Format. It belongs to Web Files category along with 303 other formats. Files using this extension can be used by programs made for Mac OS platform.
To open a .webhistory file, the full range of available software can be used. The main program to open these files is Safari browser on Mac OS X.
When double-clicked, Windows looks at the file extension to recognize file type and open in associated program. If the extension is not recognized, Windows asks to select an app to open this .webhistory file. To associate this extension with Safari browser, it needs to be added in Windows Registry.
Apple Safari
WebHistory Viewer