The dielectric environment contributes to electrostatic interaction in atomically thin (2D) semiconductors, rendering their excitons environmentally sensitive. Extended Rydberg excitons, compatible with modern semiconductor technologies and thus offering prospects for quantum simulation, quantum optics, and quantum sensing, have been observed in 2D semiconductors. How the environment affects Rydberg excitons is still poorly understood. Here we exploit a variational approach for modeling 2D Rydberg excitons within an effective mass approximation. We formulate Rydberg exciton binding energies and wave functions in their systematic relation to the dielectric contrast of the 2D semiconductor and its immediate surroundings. The model demonstrates the environmental role in determining both the overall picture of the Rydberg exciton spectrum and individual features of each. Furthermore, it provides a scaling rule for Rydberg excitons in moderate and high screening media that resembles the behavior of their conventional 2D counterparts, but is governed by a function of dielectric contrast. Available experimental observations support our model, which clarifies fundamental Rydberg exciton physics in 2D semiconductors and can be used for dielectric control of Rydberg exciton features through dielectric engineering.