Out of the box, Microsoft include a tool that you can use to do this - "RS.Exe". You can find this is folder "C:\Program Files (x86)\Microsoft SQL Server\110\Tools\Binn" - or similar depending on the SQL version and hardware you install on. This utility can be used to script most actions that are supported by reporting services. You may need to write a little VB code to go with it to actually tell it what to do.
There is another tool out there called "RS Scripter". It has become a little difficult to find of late - the site it was on no longer exists. If you can find it, it give you a graphical interface to guide and you should be able to get it to script reports out to files.