You are probably looking for something like WebConsole.

From their website:

Web Console is a web-based application that allows remote users to execute UNIX/Windows shell commands on a server, upload/download files to/from server, edit text files directly on a server and much more. The application is represented as a web page that accepts user input such as a command, executes that command on a remote web server, and shows command output in a browser. As well, simple and functional file manager build-in into the application. Web Console is open-source software written on Perl using AJAX technology. ...

This would be quick and dirty. For a more user-friendly solution, you would probably have to redesign your program interface to be web-browser/form oriented, and use CGI as others have suggested.