Your options:
Congratulations! With a vocational training completed in Germany and a binding job offer, you have a good chance of working and living in Germany.
Have you left Germany after completing your vocational training and are now living abroad?
As a citizen of Australia, Israel, Japan, Canada, the Republic of Korea, New Zealand, the United Kingdom of Great Britain and Northern Ireland or the USA, you do not require an entry visa to enter Germany. Within 90 days of being in Germany, you must apply for a residence permit for qualified employment, before taking up employment in Germany.
However, if you want to start your job shortly after entering Germany, you may want to apply for an adequate visa before entering the country. You can apply for a work visa for qualified professionals at the responsible German embassy in your country.
The following information might help you with your visa application: