Even with generational improvements in DRAM technology, memory access latency still remains the major bottleneck for application accelerators, primarily due to limitations in memory interface IPs which cannot fully account for variations in target applications, the algorithms used, and accelerator architectures. Since developing memory controllers for different applications is time-consuming, this paper introduces a modular and programmable memory controller that can be configured for different target applications on available hardware resources. The proposed memory controller efficiently supports cache-line accesses along with bulk memory transfers. The user can configure the controller depending on the available logic resources on the FPGA, memory access pattern, and external memory specifications. The modular design supports various memory access optimization techniques including, request scheduling, internal caching, and direct memory access. These techniques contribute to reducing the overall latency while maintaining high sustained bandwidth. We implement the system on a state-of-theart FPGA and evaluate its performance using two widely studied domains: graph analytics and deep learning workloads. We show improved overall memory access time up to 58% on CNN and GCN workloads compared with commercial memory controller IPs.