Ubiquitous finger motion tracking enables a number of exciting applications in augmented reality, sports analytics, rehabilitation-healthcare, haptics etc. This paper presents NeuroPose, a system that shows the feasibility of 3D finger motion tracking using a platform of wearable ElectroMyoGraphy (EMG) sensors. EMG sensors can sense electrical potential from muscles due to finger activation, thus offering rich information for fine-grained finger motion sensing. However converting the sensor information to 3D fingerposes is non trivial since signals from multiple fingers superimpose at the sensor in complex patterns. Towards solving this problem, NeuroPose fuses information from anatomical constraints of finger motion with machine learning architectures on Recurrent Neural Networks (RNN), Encoder-Decoder Networks, and ResNets to extract 3D finger motion from noisy EMG data. The generated motion pattern is temporally smooth as well as anatomically consistent. Furthermore, a transfer learning algorithm is leveraged to adapt a pretrained model on one user to a new user with minimal training overhead. A systematic study with 12 users demonstrates a median error of 6.24 degrees and a 90%-ile error of 18.33 degrees in tracking 3D finger joint angles. The accuracy is robust to natural variation in sensor mounting positions as well as changes in wrist positions of the user. NeuroPose is implemented on a smartphone with a processing latency of 0.101s, and a low energy overhead.