"The train arrived at the unloading station at Dannenberg at 9.25 am”, said a police spokesperson.
The 123 tonnes of radioactive waste will be loaded onto lorries for the final 20 kilometre stretch by road to the storage facility in Gorleben, northern Germany.
The weekend saw some violent protests as police used truncheons and charged demonstrators.
Protestors had been doing everything they could to stop the train arriving, including sitting on the rails, and even removing stones from the tracks to make them impassable. More than 3,000 people blocked the tracks on Sunday.
Shipments of radioactive waste have regularly attracted protests, but this year they have been fuelled by anger at German Chancellor Angela Merkel's aim to postpone when the country abandons nuclear power by more than a decade.
Police say they mobilised around 20,000 officers for the delivery.