How to use Mozilla Location Service as network location provider? Mozilla Location Service (MLS) can derive a location from cell towers and wi-fi networks in the vicinity, just like Google's network location service. 

But how can I configure my Android system so that it provides MLS to apps just like the Google network location service is provided now?
The MLS wiki has a list of community-provided Android software that utilizes MLS. There, you find a link to Ichnaea NLP Backend.

And that is exactly the piece of software you are looking for. Because it is an implementation of Unified NLP, the de-facto standard of non-Google network location provider services employed in Custom ROMs. See its README for installation of Unified NLP and a backend, in your case Ichnaea NLP.