The formation of interfacial moire patterns from angular and/or lattice mismatch has become a powerful approach to engineer a range of quantum phenomena in van der Waals heterostructures. For long-lived and valley-polarized interlayer excitons in transition-metal dichalcogenide (TMDC) heterobilayers, signatures of quantum confinement by the moire landscape have been reported in recent experimental studies. Such moire confinement has offered the exciting possibility to tailor new excitonic systems, such as ordered arrays of zero-dimensional (0D) quantum emitters and their coupling into topological superlattices. A remarkable nature of the moire potential is its dramatic response to strain, where a small uniaxial strain can tune the array of quantum-dot-like 0D traps into parallel stripes of one-dimensional (1D) quantum wires. Here, we present direct evidence for the 1D moire potentials from real space imaging and the corresponding 1D moire excitons from photoluminescence (PL) emission in MoSe2/WSe2 heterobilayers. Whereas the 0D moire excitons display quantum emitter-like sharp PL peaks with circular polarization, the PL emission from 1D moire excitons has linear polarization and two orders of magnitude higher intensity. The results presented here establish strain engineering as a powerful new method to tailor moire potentials as well as their optical and electronic responses on demand.