An electric propulsion system, an electric bicycle, and a method for converting a non-electric bicycle into an electric bicycle are disclosed. The electric propulsion system has an electric motor with a motor output shaft rotatable about a motor shaft axis. An output end of the motor output shaft is disposed on a first side. A transmission interconnects the electric motor and a drive chain of the bicycle to transmit a drive of the electric motor to the rear wheel. The transmission has a rotatable driven member on the first side engaged with the output end and is rotated thereby. A drive sprocket on the second side and rotatable about a drive sprocket axis is connected to the driven member by a transmission shaft. The drive sprocket engages the drive chain to transmit the drive of the electric motor thereto.