This paper introduces how Microsoft achieves that. FYI!
Project Catapult aims at efficiently accelerating the computations of tasks in datacenters with the use of FPGAs. They use the "Hardware as a service" model - with the FPGAs aiding local acceleration (on the local host CPU), remote acceleration (when idle, contribute to the global pool of available resources) and also help in network acceleration.
Azure's use of FPGA is currently on: 1. some search engine works for Bing; 2. backup the datacenter's network, e.g. access controlling, flow controlling, etc.
In the future, Azure may provides FPGA acceleration as a service available for every cloud user