In spite of their rapid growth, cloud applications still heavily rely on the network communication infrastructure, whose stability and latency directly affect the quality of experience. In fact, as mobile devices need to rapidly get real-time information and files from the cloud, it becomes an extremely important factor for cloud providers to deliver a better user experience. In this paper, we specify a cloud access overlay protocol architecture, based on traffic engineering extensions of the Locator/Identifier Separation Protocol (LISP), to improve the access performance for Cloud services delivered by a distributed data center fabric. The distributed fabric offers the possibility to access the services through multiple routing locators and to migrate server virtual machines (VMs) to different locations improving access performance. We address the problem of jointly switching VM routing locators and migrating VMs across data-center sites. We propose an adaptive control framework that allows satisfying agreed-upon levels of quality of service. We evaluate the architecture on a real distributed data-center network, involving four distant LISP-enabled data-center sites in France, as compared to legacy situations with no Cloud access optimization. By emulating realistic situations we show that, by only switching the data-center routing locator, we can guarantee a better user experience with a transfer time decreased by 80%. Moreover, we show that, to react to situations when the Cloud access link between sites is disrupted or suffers excessively from packet loss, the adaptive VM migration policy can further decrease the transfer time by 40%.