Accurate prediction of agricultural crop prices is a crucial input for decision-making by various stakeholders in agriculture: farmers, consumers, retailers, wholesalers, and the Government. These decisions have significant implications including, most importantly, the economic well-being of the farmers. In this paper, our objective is to accurately predict crop prices using historical price information, climate conditions, soil type, location, and other key determinants of crop prices. This is a technically challenging problem, which has been attempted before. In this paper, we propose an innovative deep learning based approach to achieve increased accuracy in price prediction. The proposed approach uses graph neural networks (GNNs) in conjunction with a standard convolutional neural network (CNN) model to exploit geospatial dependencies in prices. Our approach works well with noisy legacy data and produces a performance that is at least 20% better than the results available in the literature. We are able to predict prices up to 30 days ahead. We choose two vegetables, potato (stable price behavior) and tomato (volatile price behavior) and work with noisy public data available from Indian agricultural markets.