Modern FPGAs often contain heterogeneous architectures and clocking resources which must be considered to achieve desired solutions. As the design complexity keeps growing, placement has become critical for FPGA timing closure. In this paper, we present an analytical placement algorithm for heterogeneous FPGAs to optimize its worst slack and clock constraints simultaneously. First, a heterogeneity-aware and memory-friendly delay model is developed to accurately and rapidly assess each connection delay. Then, a two-stage clock region refinement method is presented to effectively resolve the clock and resource violations. Finally, we develop a novel timing-based co-optimization method to generate optimized placement without any clocking violations. Compared with the state-of-the-art placer based on the advanced commercial tool Xilinx Vivado 2019.1 with the Xilinx 7 Series FPGA architecture, our algorithm achieves the best worst slack and routed wirelength while satisfying all clock constraints.