Today's data centers need efficient traffic management to improve resource utilization in their networks. In this work, we study a joint tenant (e.g., server or virtual machine) placement and routing problem to minimize traffic costs. These two complementary degrees of freedom - placement and routing - are mutually-dependent, however, are often optimized separately in today's data centers. Leveraging and expanding the technique of Markov approximation, we propose an efficient online algorithm in a dynamic environment under changing traffic loads. The algorithm requires a very small number of virtual machine migrations and is easy to implement in practice. Performance evaluation that employs the real data center traffic traces under a spectrum of elephant and mice flows, demonstrates a consistent and significant improvement over the benchmark achieved by common heuristics.