Galileo Positioning System signal receiving
You need the hardware and a library. Most GPS modules use a serial communication, and I think that also the Galileo compatible boards use serial communication. That makes them compatible with most microcontrollers and also with Arduino boards.

I could find a few shields that can be attached to an Arduino board.
This one is in development at the moment: Kickstarter shield with Galileo
This one is compatible via the serial pins: GA-001 Multi GNSS Ublox
There is a "NEO-M8N" shield and maybe one or two others.

All those boards are very new, and I don't know if they come with a library for an Arduino. Perhaps you have to wait a few months and then it should be a lot easier to buy a complete functioning module with a library.

Before buying a module, confirm that there is a library for Arduino or good documentation to write your own library.