We present multiwavelength studies of the 106.6 ms gamma-ray pulsar PSR J1907+06 near the TeV source MGRO J1908+06. Timing observations with Fermi result in a precise position determination for the pulsar of R.A. = 19h07m547(2), decl. = +06:02:16(2) placing the pulsar firmly within the TeV source extent, suggesting the TeV source is the pulsar wind nebula of PSR J1907+0602. Pulsed gamma-ray emission is clearly visible at energies from 100 MeV to above 10 GeV. The phase-averaged power-law index in the energy range E > 0.1 GeV is = 1.76 \pm 0.05 with an exponential cutoff energy E_{c} = 3.6 \pm 0.5 GeV. We present the energy-dependent gamma-ray pulsed light curve as well as limits on off-pulse emission associated with the TeV source. We also report the detection of very faint (flux density of ~3.4 microJy) radio pulsations with the Arecibo telescope at 1.5 GHz having a dispersion measure DM = 82.1 \pm 1.1 cm^{-3}pc. This indicates a distance of 3.2 \pm 0.6 kpc and a pseudo-luminosity of L_{1400} ~ 0.035 mJy kpc^2. A Chandra ACIS observation revealed an absorbed, possibly extended, compact <(4 arcsec) X-ray source with significant non-thermal emission at R.A. = 19h07m54.76, decl. = +06:02:14.6 with a flux of 2.3^{+0.6}_{-1.4} X 10^{-14} erg cm^{-2} s^{-1}. From archival ASCA observations, we place upper limits on any arcminute scale 2--10 keV X-ray emission of ~ 1 X 10^{-13} erg cm^{-2} s^{-1}. The implied distance to the pulsar is compatible with that of the supernova remnant G40.5-0.5, located on the far side of the TeV nebula from PSR J1907+0602, and the S74 molecular cloud on the nearer side which we discuss as potential birth sites.Read less <