Computational cognitive models, which formalize theories of cognition, enable researchers to quantify cognitive processes and arbitrate between competing theories by fitting models to behavioral data. Traditionally, these models are handcrafted, which requires significant domain knowledge, coding expertise, and time investment. However, recent advances in machine learning offer solutions to these challenges. In particular, Large Language Models (LLMs) have demonstrated remarkable capabilities for in-context pattern recognition, leveraging knowledge from diverse domains to solve complex problems, and generating executable code that can be used to facilitate the generation of cognitive models. Building on this potential, we introduce a pipeline for Guided generation of Computational Cognitive Models (GeCCo). Given task instructions, participant data, and a template function, GeCCo prompts an LLM to propose candidate models, fits proposals to held-out data, and iteratively refines them based on feedback constructed from their predictive performance. We benchmark this approach across four different cognitive domains -- decision making, learning, planning, and memory -- using three open-source LLMs, spanning different model sizes, capacities, and families. On four human behavioral data sets, the LLM generated models that consistently matched or outperformed the best domain-specific models from the cognitive science literature. To validate these findings, we performed control experiments that investigated (1) the contribution of the different LLM features (model size, model family, capacities); (2) the causal role of different prompt components; (3) the effect of data contamination; (4) the ability to recover ground truth models from simulated data; and (5) the total explainable variance in human behavior captured by LLM-generated models. Taken together, our results suggest that LLMs can rapidly generate cognitive models with conceptually plausible theories that rival -- or even surpass -- the best models from the literature across diverse task domains.