Real, who have smashed the La Liga scoring record, clinched their 32nd league crown and their first in four years when Gonzalo Higuain, Mesut Ozil and Cristiano Ronaldo struck in a frenetic 3-0 win at 10-man Athletic Bilbao on Wednesday.
It went some way to easing their pain after a defeat on penalties to Bayern Munich in the Champions League semi-finals last week.
Lionel Messi's record-breaking hat-trick in Barcelona's 4-1 victory at home to Malaga in the earlier kickoff had kept alive Catalan hopes of catching their bitter rivals but Real swept Europa League finalists Bilbao aside.
They have a seven-point lead with only two games left.
Mourinho becomes the first man to win league titles in his native Portugal (Porto), England (Chelsea), Italy (Inter Milan)and Spain and has ended Barca's three-year stranglehold on the title, the club where he was an assistant coach in the 1990s.
Image: Players of Real Madrid are delighted after their team won the Spanish League at the end of their Spanish La Liga soccer match, against Athletic Bilbao, at San Mames stadium in Bilbao, northern Spain, Wednesday, May 2, 2012.