If you want to constantly build the port of your program in GNU / Linux, I would recommend switching to autotools (autoconf and automake). Autoinstalls are very common and have excellent cross-compilation support. (On the other hand, a reputation for oddity has also earned.) Although there is no automatic translation from VS projects that I know of, compiling one program can be just as simple as finding all the source and header files, listing them accordingly in Makefile.am and writing down a rule for Windows objects.
If the transition to MinGW is not written in stone or a build script with two compilers, most likely go to cmake, as suggested by commentators. Although I have always considered CMake a serious pain for unattended builders (common for open source software), it has a good reputation for creating all types of build description files, such as Makefile and VS projects.
One way or another, you will have to convert your project manually. This can be quite easy for the normal structure of the project, but it needs to be done.
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