Use procmail if it is installed on your system. Put these lines in a .procmailrc file in the home directory of the user who receives the e-mail.
:0
| /path/to/your/script.php
Or you can also use a .forward file containing
"|/path/to/your/script.php"
Procmail has the advantage that it allows you to deal with more complicated filtering if your application ever requires it.
Your script.php file will read the headers and body of the e-mail from stdin.