Measurement of peculiar velocities by combining redshifts and distance indicators is a powerful way to measure the growth rate of cosmic structure and test theories of gravity at low redshift. Here we constrain the growth rate of structure by comparing observed Fundamental Plane peculiar velocities for 15894 galaxies from the 6dF Galaxy Survey (6dFGS) and Sloan Digital Sky Survey (SDSS) with predicted velocities and densities from the 2M$++$ redshift survey. We measure the velocity scale parameter $beta equiv {Omega_m^gamma}/b = 0.372^{+0.034}_{-0.050}$ and $0.314^{+0.031}_{-0.047}$ for 6dFGS and SDSS respectively, where $Omega_m$ is the mass density parameter, $gamma$ is the growth index, and $b$ is the bias parameter normalized to the characteristic luminosity of galaxies, $L^*$. Combining 6dFGS and SDSS we obtain $beta= 0.341pm0.024$, implying that the amplitude of the product of the growth rate and the mass fluctuation amplitude is $fsigma_8 = 0.338pm0.027$ at an effective redshift $z=0.035$. Adopting $Omega_m = 0.315pm0.007$ as favoured by Planck and using $gamma=6/11$ for General Relativity and $gamma=11/16$ for DGP gravity, we get $S_8(z=0) = sigma_8 sqrt{Omega_m/0.3} =0.637 pm 0.054$ and $0.741pm0.062$ for GR and DGP respectively. This measurement agrees with other low-redshift probes of large scale structure but deviates by more than $3sigma$ from the latest Planck CMB measurement. Our results favour values of the growth index $gamma > 6/11$ or a Hubble constant $H_0 > 70$,km,s$^{-1}$,Mpc$^{-1}$ or a fluctuation amplitude $sigma_8 < 0.8$ or some combination of these. Imminent redshift surveys such as Taipan, DESI, WALLABY, and SKA1-MID will help to resolve this tension by measuring the growth rate of cosmic structure to 1% in the redshift range $0 < z < 1$.
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