Can't install Homebrew on macOS Mojave; installer doesn't recognize Command Line Tools

Xcode command line tools is a separate package for Xcode

Download Command Line Tools for Xcode from developer.apple.com/download/more and install it again.

source: Installing Xcode Command Line Tools

Useful for troubleshooting

xcode-select -p

As a side answer, It’s common for there to be a slight delay when new releases are out due to traffic or Apple taking 12 to 36 hours to seed all the download servers with a new package. Waiting a short term and retrying often works.

/usr/bin/sudo /usr/bin/xcode-select --install

Then install button in the window

An internet connection is needed and the tools will update like other system updates. You don’t need the Mac App Store or developer downloads for this to work.