Low viscosity biodegradable polymer solutions of a liquid biodegradable polymer and biocompatible solvent and methods using the compositions to form a biodegradable liquid polymer implant are provided. Liquid biodegradable polymers are dissolved in non-toxic biocompatible organic solvents to form low viscosity solutions that can be easily injected into the body with standard syringes and small gauge needles. Once the liquid polymer solution is placed within the body, the solvent dissipates or diffuses away from the polymer leaving a more viscous liquid polymer implant suitable, for example, for delivery of a biologically active agent or for use as a medical or surgical device. Because the polymer composition is a low viscosity liquid, it can be injected into muscle or subcutaneous tissue without damage to the surrounding tissue and without the noticeable bump observed with solid implant.