Europe has played a major role in dog evolution, harbouring the oldest uncontested Palaeolithic remains and having been the centre of modern dog breed creation. Here we sequence the genomes of an Early and End Neolithic dog from Germany, including a sample associated with an early European farming community. Both dogs demonstrate continuity with each other and predominantly share ancestry with modern European dogs, contradicting a previously suggested Late Neolithic population replacement. We find no genetic evidence to support the recent hypothesis proposing dual origins of dog domestication. By calibrating the mutation rate using our oldest dog, we narrow the timing of dog domestication to 20,000-40,000 years ago. Interestingly, we do not observe the extreme copy number expansion of the AMY2B gene characteristic of modern dogs that has previously been proposed as an adaptation to a starch-rich diet driven by the widespread adoption of agriculture in the Neolithic.