Semiconducting quantum wells have enabled revolutionary applications in diode lasers, IR photodetectors, and optical modulators. Recently, van der Waals (vdW) quantum wells have emerged as a promising frontier, offering inherently atomically sharp interfaces and facile integration into device structures without the constraints of lattice matching. Tunability of intersubband transitions is essential for applications of quantum wells but remains unexplored in vdW structures. Here, we report valley-selective, electric-field-activated electronic Raman scattering from intersubband transitions in natural WSe₂ multilayers and demonstrate electrical tunability by over 100 meV. We validate the generality of such tunability in 3 to 7 layers of WSe₂ and quantify the effective dipole moments and polarizabilities that determine the quantum-confined Stark effect. These intersubband transitions are also found in artificially stacked multilayers, where they can be manipulated by twist angle. Our work lays foundations for exploiting vdW quantum wells in next-generation optoelectronic applications, including tunable photodiodes and atomically compact IR spectrometers.