Apple - Can't update Developer Tools on Mojave

I faced the same problem. The way I have solve the issue is given below.

1. I got the new xcode 10.1 from App Store. Though the problem existed.
2. Then I run xcode-select --install which didn’t work.
3. I update my homebrew by brew update. Than I run sudo xcode-select --reset.

Now it works fine.

I'm the original poster. In the end I resolved the problem by installing the tools manually, with the installer I downloaded from https://developer.apple.com/download/more/.