The noise regulations around the major airports and rocket launching stations due to the environmental concern have made jet noise a crucial problem in the present day aeroacoustics research. Acoustic studies reveal that addition of chevrons to the nozzle reduces the sound pressure level reasonably with acceptable reduction in performance. In this paper three-dimensional jet acoustic characterization and geometry optimization of chevron nozzles have been carried out for getting optimum performance of the propulsion systems by meeting the multifold objectives. The numerical studies have been carried out using a validated steady 3D density based, k-ε turbulence models with standard wall functions. In the numerical study, a fully implicit finite volume scheme of the compressible, Navier-Stokes equations is employed. We observed through the parametric analytical studies that a case with round edge chevron nozzle having aerodynamically contoured tips is better than sharp edge chevrons for jet noise reduction in terms of tip effect induced noise. We also observed that round-shaped chevron nozzle could reduce ~ 4 % acoustic level with marginal thrust loss while comparing a case with conventional CD nozzle. We have proved conclusively that the geometry optimization of chevron nozzles with aerodynamically efficient tip contours for facilitating silent exit flow will enable an appreciable reduction of the jet noise at different frequencies and at different range of exit Mach numbers without much compromising on the overall performance of the aerospace vehicles. We also concluded that the chevron with round edge having suitable number of chevrons with aerofoil shaped tip contours, as the case may be, is the best choice for the sound reduction on the order of 6.5 dB with a marginal penalty of ~0.58 % total thrust loss while comparing with those aerospace vehicles having conventional CD nozzle.