In the present work, we reconstruct different f(T )-gravity models corresponding to the original and entropy-corrected versions of the holographic and new agegraphic dark energy models.We also obtain the equation of state parameters of the corresponding f(T )-gravity models. We conclude that the original holographic and new agegraphic f(T )-gravity models behave like the phantom or quintessence model, whereas in the entropy-corrected models, the equation of state parameter can justify the transition from the quintessence state to the phantom regime as indicated by the recent observations.