I am not a German national but am living and working in Germany with a valid residence permit. Can my spouse ....
...who is also not a German national live and work with me in Germany?
If you want to live in Germany with your spouse you have to submit an application for family reunification to the competent German mission abroad. You can find out more here:
EU citizens as well as citizens of Iceland, Liechtenstein, Norway and Switzerland citizens have the right to live and work in Germany. After arrival, they just need to register with the appropriate office of the town hall (mostly called "Einwohnermeldeamt" or "Bürgeramt") of their residence in Germany.