You need a different glovebox to accomodate the CD changer - available from your local Audi dealer.
I swapped my glovebox - it takes about 5 minutes to get the glovebox out (remember to disconnect the wires to the light), another 5 minutes to swap the lock from your old glovebox & swap the light & switch wiring and another 5 minutes to re-fit the new glovebox (remember to reconnect the wires to the light).
To remove the glovebox pop off the side trim and remove 5 screws (more on US models), if you've got the coolbox then unscrew the outlet from the hose, then the glovebox drops into the footwell.
Swap the wiring and light (and lock if you have a lockable glovebox - it's held in by a single screw) into the CD changer glovebox, route the CD changer cable into the CD changer slot at the top of the glovebox, refit the 5 (or more) screws and pop the side trim back on (and refit the coolbox outlet onto the hose if applicable). Then plug in the CD changer and slot the CD changer in.