Pyrochlore compounds exhibit a variety of exotic magnetic properties due to the lattice structure which can foster frustration. Particularly interesting among them is Yb₂Ti₂O₇, which orders ferromagnetically with a first-order transition. We have measured the specific heat and magnetization of Yb₂Ti₂O₇ in magnetic fields along the [100] and [110] directions. At zero field, the specific heat exhibits a sharp peak at T_c = 0.21 K, indicative of a transition to an ordered phase. The H-vs-T phase boundary for H ‖ [110] has an unusual shape, shifting to low temperatures with increasing field, similar to that reported for H ‖ [111]. Our classical Monte Carlo simulations reveal that a first-order transition occurs at 0.27 K, in good agreement with experiment, whereas the mean-field calculation yields T_c = 3.0 K, very close to the temperature of a broad hump in the specific heat. Exact calculations at T = 0 and simulations show that the magnetic ground state of Yb₂Ti₂O₇ is a simple collinear ferromagnet with negligible canting, although the spins form a “two-in-two-out” canted ferromagnetic structure with a canting angle of 19°. The transition becomes continuous in a [110] field, whereas it remains first order in [111] fields down to T = 0.