We generate the peculiar velocity field for the Two Micron All-Sky Redshift Survey (2MRS) catalog using an orbit-reconstruction algorithm. The reconstructed velocities of individual objects in 2MRS are well correlated with the peculiar velocities obtained from high-precision observed distances within 3000 km s^-1. We estimate the mean matter density to be Ω_m = 0.31 ± 0.05 by comparing observed to reconstructed velocities in this volume. The reconstructed motion of the Local Group in the rest frame established by distances within 3000 km s^-1 agrees with the observed motion and is generated by fluctuations within this volume, in agreement with observations. Having tested our method against observed distances, we reconstruct the velocity field of 2MRS in successively larger radii, to study the problem of convergence toward the cosmic microwave background (CMB) dipole. We find that less than half of the amplitude of the CMB dipole is generated within a volume enclosing the Hydra-Centaurus-Norma supercluster at around 40 h ^-1 Mpc. Although most of the amplitude of the CMB dipole seems to be recovered by 120 h ^-1 Mpc, the direction does not agree and hence we observe no convergence up to this scale. Due to dominant superclusters such as Shapley or Horologium-Reticulum in the southern hemisphere at scales above 120 h ^-1 Mpc, one might need to go well beyond 200 h ^-1 Mpc to fully recover the dipole vector. We develop a statistical model which allows us to estimate cosmological parameters from the reconstructed growth of convergence of the velocity of the Local Group toward the CMB dipole motion. For scales up to 60 h ^-1 Mpc, assuming a Local Group velocity of 627 km s^-1, we estimate Ω_m h ² = 0.11 ± 0.06 and σ₈ = 0.9 ± 0.4, in agreement with WMAP5 measurements at the 1σ level. However, for scales up to 100 h ^-1 Mpc, we obtain Ω_m h ² = 0.08 ± 0.03 and σ₈ = 1.0 ± 0.4, which agrees at the 1σ to 2σ level with WMAP5 results.