Neutron scattering measurements show the ferromagnetic XY pyrochlore Yb2Ti2O7 to display strong quasi-two dimensional (2D) spin correlations at low temperature, which give way to long range order (LRO) under the application of modest magnetic fields. Rods of scattering along < 111 > directions due to these 2D spin correlations imply a magnetic decomposition of the cubic pyrochlore system into decoupled kagome planes. A magnetic field of ~0.5 T applied along the [1-10] direction induces a transition to a 3D LRO state characterized by long-lived, dispersive spin waves. Our measurements map out a complex low temperature-field phase diagram for this exotic pyrochlore magnet.