The Seebeck and Nernst coefficients S and ν of the cuprate superconductor YBa2Cu3Oy (YBCO) were measured in a single crystal with doping p=0.12 in magnetic fields up to H=28T. Down to T=9 K, ν becomes independent of field by H 30T, showing that superconducting fluctuations have become negligible. In this field-induced normal state, S/T and ν/T are both large and negative in the T→0 limit, with the magnitude and sign of S/T consistent with the small electronlike Fermi surface pocket detected previously by quantum oscillations and the Hall effect. The change of sign in S(T) at T 50 K is remarkably similar to that observed in La2-xBaxCuO4, La2-x-yNdySrxCuO4, and La2-x-yEuySrxCuO4, where it is clearly associated with the onset of stripe order. We propose that a similar density-wave mechanism causes the Fermi surface reconstruction in YBCO. © 2010 The American Physical Society.