In distributed network applications, e.g., the Internet of Things (IoT), any drift in the clock on a single node can cause cascading effects detrimental to the systems that involve ordered events and time critical tasks. To provide a stable reference clock, time synchronization protocols are deployed where a slave node can synchronize its clock with a master node. IEEE 1588 Precision Time Protocol (PTP) is increasingly becoming popular for its high time synchronization accuracy. However, it was primarily designed for high-speed wired communication networks. In this paper, we propose complete design and FPGA implementation of IEEE 1588 PTP for deployment in low-speed and low data-rate Bluetooth communication medium. Experimental results show synchronization accuracy in the range of few nanoseconds (ns) which is around three orders of magnitude better than the existing synchronization techniques used in Bluetooth-based wireless networks.