High accuracy in production parts and manufacturing quality are the requirements of production. Residual stress affects the surface quality and dimensional accuracy of manufactured parts. Production of parts with geometric tolerance, optimal residual stress, and suitable surface quality is always required by manufacturing industries. When machining parts, tensile residual stresses are created in them, which is one of the main reasons for the loss of geometric tolerances and distortion in the workpiece. This study investigated the effect of the ultrasonic-assisted vibration compared with conventional machining in various conditions of a 2024 aluminum workpiece on the surface quality, runout, straightness, and tensile residual stresses. In this article, the effects of geometric tolerance parameters, tensile residual stress, and surface roughness have been investigated simultaneously. A total of 18 experiments in different cutting speeds and feed rates in two machining states of conventional and ultrasonic vibration states were performed. The results showed that ultrasonic vibrations could be used to achieve 31% lower run out and 36% lower straightness in the parts. Also, the values of tensile residual stress in the ultrasonic vibration machining were 11% lower compared to conventional machining. Ultrasonic vibrations can also be used in most cases to achieve better surface quality, tolerance, and tensile residual stress according to machining parameters compared to conventional machining. The experimental results show that ultrasonic-assisted turning is a reliable method for machining, which can obtain lower tensile residual stress and improve the machined surface integrity and better tolerances.