There is a wide range of science and applications accessible via the strain engineering of quantum transport in 2D materials. We propose a realistic experimental platform for uniaxial strain engineering of ballistic charge transport in graphene. We then develop an applied theoretical model, based on this platform, to calculate charge conductivity and demonstrate graphene quantum strain transistors (GQSTs). We define GQSTs as mechanically strained ballistic graphene transistors with on/off conductivity ratios > 10 4 , and which can be operated via modest gate voltages. Such devices would permit excellent transistor operations in pristine graphene, where there is no band gap. We consider all dominant uniaxial strain effects on conductivity, while including experimental considerations to guide the realization of the proposal. We predict multiple strain-tunable transport signatures, and demonstrate that a broad range of realistic device parameters lead to robust GQSTs. These devices could find applications in flexible electronic transistors, strain sensors, and valleytronics.