The Andalusian club have paid a reported €13.5m plus €1.5m in variables for 22-year-old Rodriguez.
Madrid initially wanted €20m for Rodriguez, but lowered their asking price in return for a 25% sell-on clause.
Los Blancos will also have a first refusal on their academy product in the years ahead.
— Sevilla Fútbol Club (@SevillaFC) August 29, 2020
The Spain under-21 talent impressed in his two seasons on loan at Leganes, leading to several clubs expressing interest.
Sevilla coach Julen Lopetegui and sporting director Monchi identified Rodriguez as a suitable replacement for Ever Banega.
Rodriguez, who can play in various midfield positions, is Sevilla’s first signing of the transfer window.