DNN accelerators are often developed and evaluated in isolation without considering the cross-stack, system-level effects in real-world environments. This makes it difficult to appreciate the impact of System-on-Chip (SoC) resource contention, OS overheads, and programming stack inefficiencies on overall performance/energy-efficiency. To address this challenge, we present Gemmini, an open-source, full-stack DNN accelerator generator. Gemmini generates a wide design-space of efficient ASIC accelerators from a flexible architectural template, together with flexible programming stacks and full SoCs with shared resources that capture system-level effects. Gemmini-generated accelerators have also been fabricated, delivering up to three orders-of-magnitude speedups over high-performance CPUs on various DNN benchmarks.