The T2K experiment is designed to study neutrino oscillation properties by directing a high intensity neutrino beam produced at J-PARC in Tokai, Japan, towards the large Super-Kamiokande detector located 295 km away, in Kamioka, Japan. The experiment includes a sophisticated near detector complex, 280 m downstream of the neutrino production target in order to measure the properties of the neutrino beam and to better understand neutrino interactions at the energy scale below a few GeV. A key element of the near detectors is the ND280 tracker, consisting of two active scintillator-bar target systems surrounded by three large time projection chambers (TPCs) for charged particle tracking. The data collected with the tracker is used to study charged current neutrino interaction rates and kinematics prior to oscillation, in order to reduce uncertainties in the oscillation measurements by the far detector. The tracker is surrounded by the former UA1/Nomad dipole magnet and the TPCs measure the charges, momenta, and particle types of charged particles passing through them. Novel features of the TPC design include its rectangular box layout constructed from composite panels, the use of bulk micromegas detectors for gas amplification, electronics readout based on a new ASIC, and a photoelectron calibration system. This paper describes the design and construction of the TPCs, the micromegas modules, the readout electronics, the gas handling system, and shows the performance of the TPCs as deduced from measurements with particle beams, cosmic rays, and the calibration system.