Topological insulators are anticipated to be a viable option for flexible near-infrared (NIR) photodetection that is a basic potential comportment for future photoelectric applications, wearable devices, and potential defence applications. Here we report the fabrication of a flexible NIR photodetector using Bi2Te3 thin film deposited on flexible polyethylene terephthalate (PET) substrate and an investigation of strain effects on the photocurrent both experimentally and theoretically via density functional theory. These flexible optoelectronic devices exhibit bandgap modulation which is governed by the strain under various bending angles and bending cycles. We report that the electronic bandgap of thin film of Bi2Te3 on flexible PET substrate reduces with increased compressive lattice strain upon bending. The fabricated devices exhibit ultra-high photoresponsivity and detectivity of 220 A/W and 1.6 × 10^(10) Jones, respectively, upon bending at angle (80°), which is >3 times as compared to no-strain condition, i.e. without bending. The robustness and stability of these devices were ascertained by studying the bias-dependent photoresponse under NIR (1064 nm) illumination at various strains upon bending (angles 0°, 60°, 80°, 100° and 120°), after being bent repeatedly (0, 1, 100, 500 and 1000 cycles) with 80° bending angle. Besides being flexible, our results show that these devices exhibit high stability under various bending cycles. Hence, this research can play a pivotal role for the construction of high-performance, affordable and flexible optoelectronic devices in the future.