you already tagged "XDK" which would be a means.
Otherwise you could also use a Java API with websocket support.
My 2 cents
This tutorial goes over how to control a Galileo/Edison board with an Android app (via bluetooth).
Bluetooth* LE (BLE) communication use is exploding both in commercial products and hobby applications, mainly due to its low-cost and low-power requirements. This makes it an excellent choice when you want to communicate from your Android* phone or tablet to your Intel® Edison or Intel® Galileo projects.
The goal of this document is to show you how to write code and connect the hardware to establish BLE communication between an Intel Edison and a Bluetooth 4.0-equipped Android device, using free software tools and low-cost, off-the-shelf hardware.