Physical Unclonable Functions (PUFs) are used for securing electronic designs across the implementation spectrum ranging from lightweight FPGA to server-class ASIC designs. However, current PUF implementations are vulnerable to model-building attacks; they often incur significant design overheads and are challenging to configure based on application-specific requirements. These factors limit their application, primarily in the case of the system on chip (SoC) designs used in diverse applications. In this work, we propose MeL-PUF - Memory-in-Logic PUF, a low-overhead, distributed, and synthesizable PUF that takes advantage of existing logic gates in a design and transforms them to create cross-coupled inverters (i.e. memory cells) controlled by a PUF control signal. The power-up states of these memory cells are used as the source of entropy in the proposed PUF architecture. These on-demand memory cells can be distributed across the combinational logic of various intellectual property (IP) blocks in a system on chip (SoC) design. They can also be synthesized with a standard logic synthesis tool to meet the area,power, or performance constraints of a design. By aggregating the power-up states from multiple such memory cells, we can create a PUF signature or digital fingerprint of varying size. We evaluate the MeL-PUF signature quality with both circuit-level simulations as well as with measurements in FPGA devices. We show that MeL-PUF provides high-quality signatures in terms of uniqueness, randomness, and robustness, without incurring large overheads. We also suggest additional optimizations that can be leveraged to improve the performance of MeL-PUF.