Electric Vehicles (EVs) with single-ratio gearbox provide high levels of smoothness, but using multi-speed gearbox can provide significant benefits in terms of vehicle acceleration, top speed, powertrain cost, mass, and energy consumption. In particular, Automated Manual Transmissions (AMTs) have characteristics of smooth shifts without torque interruption when coupled to a torque bypass clutch. However, conventional friction clutches are not best suited as torque bypass clutches because of their limited controllability and because large amount of heat must be dissipated to slow down the motor during gearshifts. This paper studies the feasibility of a seamless AMT architecture for EVs and Hybrid Electric Vehicles (HEVs) using an eddy current torque bypass clutch that is highly controllable, robust, low cost, and has no wearable parts. A system-level study using a backward-facing model is used to assess the advantages of multi-speed gearboxes for EVs in terms of energy consumption, powertrain cost, and mass. A full-scale clutch prototype is designed for a custom two-speed AMT of an 80 kW EV. Numerical simulations show that a two-speed gearbox can improve energy consumption by 7.2 % for a compact class EV such as the Nissan Leaf. Moreover, using two gear ratios allows a downsizing of the electric motor, which could reduce powertrain cost and mass by 23.1 % and 15.6 %, respectively. The clutch is characterized experimentally and its maximum torque agrees well with analytical results (within 6 %). The prototype performed a seamless shift on a test bench demonstrating the viability of using an eddy current clutch for torque bypass clutches in AMTs.