What do I need to convert my EXE to be a MSI installer application?

We have an application that must be be installed and deinstalled using VBScripts we have written in-house.  To install a new release we first have to run a deleteapp script to rip out any old verision that may exist.  After the old version has been removed files have to pushed down to a specific folder and then the Installapp script is run to hook the deployed files into system.  To make a long story short, we found a freeware utility called INNO Setup that has allowed us to create a single SETUP.EXE file.  When SETUP is executed it deploys all needed files to the C:\temp folder, executes the delete script, unzips the application files to the correct folder, runs the installation script and then removes the files from the temp folder.  The problem we have is that a particular area of the company cannot use our regular software deployment tool and they are attempting to use Microsoft Windows Group Policy Installer methodology that requires that the package be in an MSI format, not an EXE format.  I've been searching so far in vain for a utility to convert an EXE into an MSI and nothing seems to work like we want it to.  In our situation all we need to do is have the MSI installer deploy and execute the setup.exe on the target or does what the setup file does in the order in which things need to be done.  It would also be helpful if I could find something that was freeware as well.  Any help would be appreciated.