The main objective of this paper is the conceptual design of a computational AI system that emulates human creativity. To do this, extensive research has been done on recent discoveries about the neural bases of human creativity. As a result, eleven neurocognitive factors have been identified on which the tremendous creative capacity of the human brain is based. The integration of these factors has made it possible to create a neurocognitive model of human creativity. The analysis of each of creative neurocognitive structures separately suggests certain characteristics that must be present in the structure of a creative computational system to emulate brain creativity. Properly integrating these characteristics, a general architecture for a creative multi-agent system has been proposed, as well as the guidelines for the correct representation of knowledge. Based on this general architecture a creative computational system can be implemented for a specific field of knowledge, or general purpose.