Coherently integrating echoes of multiple-input-multiple-output (MIMO) radar could enhance detection performance and early warning capability for high-speed weak targets. Nevertheless, the echo signal integration incorporating the single channel and multichannel faces two major challenging problems: first, the across range unit (ARU) is caused by the high-speed motion of targets for single-channel returns, and second, the echo envelope and phase differences between channels make multichannel integration particularly difficult. To tackle these issues, we propose a multichannel signal integration approach for high-speed weak target detection in coherent MIMO radar system. More precisely, we establish the echo model for the high-speed target with MIMO radar, and the Radon Fourier transform (RFT) is used to accumulate the single-channel returns with ARU. Then, we analyze the output characteristics of RFT with respect to different channels. Further, aiming to achieve multichannel integration, we decompose it into two steps: intranode integration and internode integration. First, by exploiting the target kinematic constraint and spatial geometric relations between MIMO radar nodes and the target, we propose the intranode integration algorithm, wherein we derive the target's energy accumulation equations among channels. After that, based on the properties of the intranode integration, we further propose the internode integration algorithm. Ultimately, the multichannel coherent accumulation is obtained, and the theoretical integration output responses of intranode and internode are provided in detail, respectively. Through numerous simulation experiments, we demonstrate the feasibility of the proposed approach.