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. = 19(h)07(m)54.(s)7(2), decl. = +06 degrees 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 Gamma = 1.76 +/- 0.05 with an exponential cutoff energy E-c = 3.6 +/- 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 similar or equal to 3.4 mu Jy) radio pulsations with the Arecibo telescope at 1.5 GHz having a dispersion measure DM = 82.1 +/- 1.1 cm(-3) pc. This indicates a distance of 3.2 +/- 0.6 kpc and a pseudo-luminosity of L-1400 similar or equal to 0.035 mJy kpc(2). A Chandra ACIS observation revealed an absorbed, possibly extended, compact (less than or similar to 4 '') X-ray source with significant nonthermal emission at R.A. = 19(h)07(m)54.(s)76, decl. = + 06 degrees 02'14.'' 6 with a flux of 2.3(-1.4)(+0.6) 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 similar to 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.
