In e-commerce fulfillment warehouses, manual item picking is a labor-intensive and tedious task. Therefore, automation of item picking can improve efficiency and save cost for e-commerce businesses. This paper presents an automated robot picking solution that meets the requirements of automating the picking of items from shelves. The hardware of the proposed system comprises a lightweight robot manipulator, a low-cost commercially available 3D camera system and a custom-built robotic gripper. The software of the proposed system is modular comprising the task planning module, item identification and registration modules, grasp planning module and the motion planning modules. Simulations are carried to illustrate full cycles of the automated picking of items. Experiments were conducted using a prototype of the proposed system. The test results show the system is capable of picking several regularly-shaped and irregularly-shaped items from the bins of the shelf. Such preliminary observations prove the system to be flexible and versatile. It has the potential to be used in real e-commerce fulfillment warehouses.