Grippers developed in recent years either cannot achieve a complete universality due to grasping stability issues or are designed with excessive complexity. In this paper, the design of a three-fingered tendon-driven integrated gripper based on the concept of integrating Universal Active Gripper (UAG) with Universal Passive Gripper (UPG) fingertips, which ensures achieving adjustable fingertip stiffness and is practically proven to solve grasping stability issues, is proposed. Furthermore, kinematic, dynamic, and force analyses was conducted to calculate the specifications of the designed gripper, which was compared to four commercial grippers. Finite element analysis was also carried out for the designed gripper. When the final design of the gripper was compared to that of Hou et al.'s (2018) (the only comparable design present for the integrated gripper), one crucial similarity noted was based on both designs adopting the same kinematic configuration. This fact further increases the confidence in the optimal development of the designed gripper. According to FEA results, the maximum stress acting on the components of the gripper was 15.78 MPa, 39.45% of the yield stress of Acrylonitrile Butadiene Styrene (ABS). In conclusion, it was theoretically established that the designed gripper with the tendon-driven actuation is operating efficiently.