The 400-MeV proton linear accelerator (LINAC) at the Japan Proton Accelerator Research Complex (J-PARC) consists of 324-MHz low-β and 972-MHz high-β accelerator sections. From October 2006 to May 2013, only the 324-MHz low-β accelerator section was in operation. From the summer of 2013 the J-PARC LINAC was upgraded by installing the 972-MHz high-β accelerator section, and the proton beam was successfully accelerated to 400MeV in January 2014. Auto-tuning systems for the J-PARC LINAC RF cavities have been successfully developed. A first generation design, an auto-tuning system using a mechanical tuner controller, was developed and operated for the first 3 years. Then the second-generation auto-tuning system was developed using a new approach to the RF cavity warm-up process, and this was applied to the accelerator operation for the subsequent 4 years. During the RF cavity warm-up process in this system, the mechanical tuner is constantly fixed and the input RF frequency is automatically tuned to the cavity resonance frequency using the FPGA (Field-Programmable Gate Array) of the digital feedback RF control system. After the input power level reaches the required value, input RF frequency tuning is stopped and it is switched to the operation frequency. Then, the mechanical tuner control begins operation. This second-generation auto-tuning system was extremely effective for the 324-MHz cavity operation. However, if we apply this approach to the 972-MHz RF cavities, an interlock due to the RF cavity reflection amplitude occasionally occurs at the end of the warm-up process. In order to solve this problem a third generation novel auto-tuning system was successfully developed in December 2013 and applied to the operation of the J-PARC LINAC, including the 972-MHz ACS RF cavities. During the warm-up process both the mechanical tuner controller and the input RF frequency tuning are in operation, and good matching between the input RF frequency and the RF cavity is obtained during the entire warm-up process. As a result of their excellent performance, 972-MHz ACS cavity operation and the J-PARC LINAC 400MeV upgrade have been successfully implemented. In this paper, the development of the auto-tuning systems and their applications will be described in detail.