If you have access to the GAC on the server, then just abstract the code out of the EXE and into a library assembly. Add the library DLL to the GAC. Then reference that DLL from both the EXE and the Web project.
If you don't have access to the GAC you can still do it, just deploy the DLL with the EXE and in your web app's bin.
EDIT
here's how to create a library assembly http://broadcast.oreilly.com/2010/07/understanding-c-namespaces-and.html