Densely-deployed Content Delivery Network (CDN) solutions are used today for delivering a significant fraction of the Internet traffic through replication mechanisms. However, these networks show technological limitations when dealing with the proliferation of rich media-enabled applications such as video streaming. This paper introduces a new approach to content delivery incorporating Information-Centric Networking principles without requiring any change in the underlying network. This solution improves content delivery performance and enables the implementation of cost efficient request routing strategies. We also develop an on-line algorithm based on Lyapunov optimization theory which allows to dynamically generate effective strategies in order to satisfy operator's objectives. By using real video streaming request traces, it has been shown that the global hit ratio can be increased up to 100\% while delivering the content 30\% faster compared to currently deployed content delivery schemes. Furthermore, the proposed approach offers stable behavior during peak traffic.