In this work we analyse the ways in which public procurement can encourage business innovation by supporting the formation of markets for new products, technologies and services. We use an evolutionary analytical framework in which markets for innovation are defined as dynamic complex systems whose function is the creation and coordination of knowledge as they develop over time. We show that public procurement has a key role in supporting this function throughout all the stages in the process of market development, and identify specific tools and actions that can be implemented at different phases of the procurement cycle to do so. We illustrate the main conceptual arguments of our analysis with examples from existing case studies on the public procurement of innovations.