Living in another EU country does not automatically give a non-EU citizen the right to move to Germany and start working there. What matters is the residence status you currently hold, whether you have EU long-term resident status, an EU Blue Card or another national permit, and what you plan to do after moving.
This article explains the main routes for moving to Germany from another EU country, including the special mobility rules for EU Blue Card holders and EU long-term residents. It also looks at the important difference between having permission to live in one EU country and having EU freedom of movement.