We present measurements of the velocity power spectrum and constraints on the growth rate of structure ƒσ8, at redshift zero, using the peculiar motions of 2,062 galaxies in the completed 2MASS Tully-Fisher survey (2MTF). To accomplish this we introduce a model for fitting the velocity power spectrum including the effects of non-linear Redshift Space Distortions (RSD), allowing us to recover unbiased fits down to scales k = 0.2 h Mpc-1 without the need to smooth or grid the data. Our fitting methods are validated using a set of simulated 2MTF surveys. Using these simulations we also identify that the Gaussian distributed estimator for peculiar velocities of Watkins & Feldman (2015) is suitable for measuring the velocity power spectrum, but sub-optimal for the 2MTF data compared to using magnitude fluctuations δm, and that, whilst our fits are robust to a change in fiducial cosmology, future peculiar velocity surveys with more constraining power may have to marginalise over this. We obtain scale-dependent constraints on the growth rate of structure in two bins, finding ƒσ8 = [0.55 +0.16 -0.13, 0.40 +0.16 -0.17] in the ranges k = [0.007-0.055, 0.55-0.150] h Mpc-1. We also find consistent results using four bins. Assuming scale-independence we find a value ƒσ8 = 0.51 +0.09 -0.08, a ∼16% measurement of the growth rate. Performing a consistency check of General Relativity (GR) and combining our results with CMB data only we find γ = 0.45 +0.10 -0.11, a remarkable constraint considering the small number of galaxies. All of our results are completely independent of the effects of galaxy bias, and fully consistent with the predictions of GR (scale-independent ƒσ8 and γ ≈ 0.55).