With the prevalence of location-based services and geo-functioned devices, the trend of spatial data outsourcing is rising. In the data outsourcing scenario, result integrity must be ensured by means of a query authentication scheme. However, most of the existing studies are confined to a centralized environment. In this paper, we investigate the query authentication problem in distributed environments and focus on the k nearest neighbor (kNN) query, which is widely used in spatial data analytics. We design a new distributed spatial authenticated data structure (ADS), distributed MR-tree, to facilitate efficient kNN processing. Furthermore, we propose a basic algorithm to process authenticated kNN queries based on the new ADS. Apart from the results, some verification objects are generated to guarantee the results' integrity. We also design two optimized algorithms to reduce the size of verification objects as well as the verification cost. Our experiments validate the good performance of the proposed techniques in terms of query cost, communication overhead, and verification time.