Real who lead the points tally in the top division soccer league with 86 points after 37 games, have an unassailable seven point lead over second placed and arch rivals Barcelona, who were beaten 2-1 at home to Osasuna.
Real were put in the lead in the 29 minute after Benzema fired one shot through the legs of goal keeper Sergio Asenjo. The goal poacher then converted a penalty in the 77th to help Real on their way to a remarkable 10th consecutive league win since the season resumed after the COVID-19 stoppage.
After the match Real captain Ramos hoisted the Liga trophy into the air at the empty Alfredo di Stefano stadium, where the Madrid side have been playing their final games of the season while their Santiago Bernabeu home is being renovated.
"To return after spending three months locked in our homes and to win 10 matches in a row is incredible, but I always believed in my team and knew we could win it," said Real goalkeeper Thibaut Courtois.
Elsewhere, goals from Marcos Llorente and Thomas Partey gave Atletico Madrid a 2-0 win away to Getafe to keep them firmly in third, while Sevilla's 0-0 draw away to Real Sociedad means they will finish at least in fourth.
Those two results means that both Getafe and Real Sociedad still have work to do to assure a place in next season's Europa League, after Valencia beat already relegated Espanyol 1-0 thanks to a Kevin Gameiro goal and Granada came back from a goal down to win 2-1 away to relegation-bound Mallorca.