The primary mechanism of operation of almost all transistors today relies on the electric-field effect in a semiconducting channel to tune its conductivity from the conducting 'on' state to a non-conducting 'off' state. As transistors continue to scale down to increase computational performance, physical limitations from nanoscale field-effect operation begin to cause undesirable current leakage, which is detrimental to the continued advancement of computing1,2. Using a fundamentally different mechanism of operation, we show that through nanoscale strain engineering with thin films and ferroelectrics the transition metal dichalcogenide MoTe2 can be reversibly switched with electric-field-induced strain between the 1T'-MoTe2 (semimetallic) phase to a semiconducting MoTe2 phase in a field-effect transistor geometry. This alternative mechanism for transistor switching sidesteps all the static and dynamic power consumption problems in conventional field-effect transistors3,4. Using strain, we achieve large non-volatile changes in channel conductivity (Gon/Goff ≈ 107 versus Gon/Goff ≈ 0.04 in the control device) at room temperature. Ferroelectric devices offer the potential to reach sub-nanosecond non-volatile strain switching at the attojoule/bit level5-7, with immediate applications in ultrafast low-power non-volatile logic and memory8 while also transforming the landscape of computational architectures because conventional power, speed and volatility considerations for microelectronics may no longer exist.