The pi-pi scattering phase shifts for both the s-wave I=0 and I=2 channels are determined from a lattice calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size $32^3\times 64$. The phase shifts are determined for both stationary and moving pi-pi systems, at four different center of mass momenta. We implement several interpolating operators including a sigma operator and $\pi\pi$ operator with the pions carrying relatively larger momentum. We use both correlated fitting and the generalized eigenvalue treatment and compare these two results with dispersive predictions. A detailed excited state contamination error analysis is included.