Deep Neural Networks (DNNs) have stimulated intensive FPGA-based acceleration solutions, and multi-die FPGAs offer abundant resources for implementing large-scale DNN workloads. However, current FPGA frameworks overlook the opportunities of optimization on multi-die FPGAs. In this paper, we propose an automated framework named DNNMapper, for mapping DNNs to multi-die FPGAs. With careful consideration of the unique architectural characteristics and resource constraints of multi-die FPGAs, DNNMapper involves model partitioning and resource allocation as two critical processes that map DNN layers onto respective FPGA dies and efficiently allocate hardware resources. DNNMapper employs a co-design engine based on a genetic algorithm, which co-optimizes model partitioning and resource allocation. Experimental results demonstrate that accelerators generated by DNNMapper offer superior performance and scalability, achieving up to 2× higher throughput and 1.3× to 1.9× higher DSP density. Moreover, our accelerator demonstrates a frequency improvement from 1.28× to 1.69×.