Coherent terahertz and millimeter wave radiation from laser accelerated electron bunches has been measured. The bunches were produced by tightly focusing (spot diameter ~; 6 mu m) a high peak power (up to 10W), ultra-short (>50 fs) laser pulse from a high repetition rate (10 Hz) laser system (0.8 mu m), onto a high density (>1019 cm3) pulsed gas jet of length ~; 1.5 mm. As the electrons exit the plasma, coherent transition radiation is generated at the plasma-vacuum boundary for wavelengths long compared to the bunch length. Radiation in the 0.3 -19 THz range and at 94 GHz has been measured and found to depend quadratically on the bunch charge. The measured radiated energy for two different collection angles is in good agreement with theory. Modeling indicates that optimization of this table-top source could provide more than 100 mu J/pulse. Together with intrinsic synchronization to the laser pulse, this will enable numerous applications requiring intense terahertz radiation. This radiation can also be used as a powerful tool for measuring the properties of laser accelerated bunches at the exit of the plasma accelerator. Preliminary spectral measurements indicates that bunches as short as 30 - 50 fs have been produced in these laser driven accelerators.