We’re using CMake for Linux projects. CMake can generate KDevelop and Visual Studio project files, so you can just create your CMake file as the origin of platform-specific IDE files. The KDevelop generator is fine, so you can edit and compile in KDevelop (which will in turn call Make).
On the other hand, if you have nothing fancy, you can use CMake or just Make to build the thing on Linux, if you want to stay with your solution file (which is what I’m currently doing for a library with test applications). This approach gets complicated when your build process is more than just “throw these files at the compiler and let’s see what it does”, so the CMake solution is in my opinion a good thing for cross-platform development.