Moving iTunes library from Macs with different OS
Though maybe a bit hard to locate the relevant information in this this support article, once found, it's easy to follow. 

I would proceed as follows:

Consolidate your iTunes Library on your old machine.


Make sure the following is checked: iTunes &gt; Preferences &gt; Advanced &gt; Copy files to iTunes Media Folder when adding to Library. Click OK. Note you can also see the path of to your library in this pane. 
Next, File &gt; Library &gt; Organize Library... &gt; Consolidate Files. For earlier versions of iTunes, this may be File &gt; Library &gt; Consolidate.


Copy iTunes Library to an external Hard-drive


You can find the location of your iTunes Library from the "Advanced" pane mentioned earlier. By default, the location is ~/Music/iTunes/. Find the path from this pane, select it, and copy it using Command+C
Open Finder. Use the key combination  Shift+Command+G to bring up a "Go to folder" window. Paste the copied path here and click ok. 
Drag the folder named "iTunes" to the external HDD. Let it copy. Depending on the size of your Library, this could take a bit. Once it has completed, eject the external Hard drive


Copy iTunes Library to new computer


Connect the external hard drive to your new machine. 
Open Finder. Use the key combination  Shift+Command+G again and copy the following path, exactly as shown, into the pop-up window: ~/Music/
You will see an iTunes Folder present. Drag it into your trash. 
Next, open the external drive, and drag the iTunes folder from the external drive to the same (now empty) Music folder on the new machine. 
Open iTunes. Your original library, including the metadata (playlists, etc), should now be present on the new machine.