Stencil codes (a.k.a. nearest-neighbor computations) are widely used in image processing, machine learning, and scientific applications. Stencil codes incur nearest-neighbor data exchange because the value of each point in the structured grid is calculated as a function of its value and the values of a subset of its nearest-neighbor points. When running on Graphics Processing Unit (GPUs), stencil codes exhibit a high degree of data sharing between nearest-neighbor threads. Sharing is typically implemented through shared memories, shuffle instructions, and on-chip caches and often incurs performance overheads due to the redundancy in memory accesses. In this article, we propose Neighbor Data (NeDa), a direct nearest-neighbor data sharing mechanism that uses two registers embedded in each streaming processor (SP) that can be accessed by nearest-neighbor SP cores. The registers are compiler-allocated and serve as a data exchange mechanism to eliminate nearest-neighbor shared accesses. NeDa is embedded carefully with local wires between SP cores so as to minimize the impact on density. We place and route NeDa in an open-source GPU and show a small area overhead of 1.3%. The cycle-accurate simulation indicates an average performance improvement of 21.8% and power reduction of up to 18.3% for stencil codes in General-Purpose Graphics Processing Unit (GPGPU) standard benchmark suites. We show that NeDa’s performance is within 13.2% of an ideal GPU with no overhead for nearest-neighbor data exchange.