The car plant was delayed for eight months over local authority licensing problems.
Musk’s €5billion electric car factory is the biggest investment in a German car plant in recent history.
The electric car factory in Germany’s eastern state of Brandenburg is Tesla’s first production site in Europe, and officials are hoping it will help the region position itself as a hub for electric vehicle production.
The company aims to employ about 12,000 workers at the site who will churn out around 500,000 Model Y cars annually, the firm’s all-electric, compact SUVs.
Tesla’s arrival is expected to jolt Germany’s flagship car industry, setting the stage for fierce competition with rivals Volkswagen, BMW and Mercedes-Benz as they pivot from traditional engines to cleaner electric vehicles.
“The new era in the auto industry has now arrived in Germany too,” said analyst Ferdinand Dudenhoeffer from the Center for Automotive Research.
Tesla’s focus on Europe comes as the continent grapples with sky-high energy costs that have sent petrol prices soaring, prompting some drivers to take a closer look at electric alternatives.
Musk said: “This is a great day for the factory,” describing it as “another step in the direction of a sustainable future”.
German Chancellor Olaf Scholz said the plant was a sign of progress and the future of the car industry.
Tesla will deliver its first 30 German-made Model Y Performance cars on Tuesday. The firm says the cars have a 514km (320 miles) range and cost €63,990 (£53,000).
At full capacity, the plant will produce 500,000 cars annually – more than the 450,000 battery-electric vehicles that German rival Volkswagen sold globally in 2021.
It will also generate 50 gigawatt hours (GWh) of battery power.
For now, Volkswagen still holds the upper hand in Europe’s electric vehicle market, with a 25% market share to Tesla’s 13%.
Musk has said ramping up production will take longer than the two years it took to build the plant.