I don\'t know how to install the Command Line Tools on OSX Mavericks. Or better: I know how to do it (I just did it on another MacBook), but something goes wrong this time.
I came across this issue when I removed Xcode from my laptop (Not enough disk space) and wanted to just install the commandline tools. It installed, but did not fix the Xcode-select path. Using the information above, I then ran:
xcode-select -s /Library/Developer/CommandLineTools
Homebrew is now working great with just the command line tools and I have 9 GB back! Therefore, if you have removed Xcode from your system and just installed the command line tools, you will have to manually run the above command line.