How to import a GIT non-Eclipse Java project into Eclipse?

It is possible by first cloning the repository and then creating a General project based on that. Then you can convert it to Java project. Here is how:

• First go to File>Import...>Projects from GIT.
• In the Select a Git Repository view you first press Clone. And follow instructions. This will create a local “checkout” of the repository to your computer. You can set the folder to be your workspace so it looks like any other of your eclipse projects.
• After you have cloned the repository you get back to Import-view. Now you can select the repository you just cloned from the list.
• Click Next and select Import as General Project. Now you have a git repository to eclipse.
• Convert it to Java project: Add nature and buildCommand elements from other Java project to your .project file:

Relevant sections from .project:

<buildSpec>
    <buildCommand>
        <name>org.eclipse.jdt.core.javabuilder</name>
        <arguments>
        </arguments>
    </buildCommand>
</buildSpec>
<natures>
    <nature>org.eclipse.jdt.core.javanature</nature>
</natures>

Then from Project>Properties>Java Build Path>Source add your source folders (and possible libraries).

Edit: Added the conversion to Java project.