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 kick-off 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.
"It has been a very long and hard season but we have taken a step forward in terms of quality compared to last year," Real captain Iker Casillas said in a television interview.
"It was tough to end Barca's run as this is a new project and we are a young squad but I think we already improved last year and even more so this year," added the Spain goalkeeper, as his team mates celebrated wildly on the pitch nearby.
Real have only lost twice all season, 1-0 at Levante and 3-1 at home to Barca, and have amassed a record 115 goals with 30 conceded.
Their success has been largely down to the awesome firepower of their front line, with Ronaldo racking up 44 goals, Higuain netting 22 and Karim Benzema 20, the first time three players from the same club have passed the 20 mark.
Mourinho also gave an expensively-assembled group of players the self-belief that allowed them to get the better of Barca, widely regarded as one of the best teams of all time.
Barca's home form let them down and they dropped 16 points on their travels to Real's seven before a 2-1 defeat by Real in the 'Clasico' at the Nou Camp last month effectively ended their title bid.
"We are very happy after winning a very closely-fought championship against a very strong Barcelona," defender Sergio Ramos said.
"Madrid deserve the title and we dedicate it to all the fans."
BLISTERING START
The match at the San Mames got off to a blistering start, with both sides pouring forward in search of a goal.
Real should have been ahead in the 12th minute when the referee ruled Javi Martinez had handled the ball in the area and awarded a penalty.
Ronaldo, who missed a spot-kick in the Champions League semi-final shootout against victorious Bayern Munich last week, attempted a dinked shot down the middle of the goal and goalkeeper Gorka Iraizoz diverted the ball over the bar.
It was the first time the Portuguese had fluffed a penalty in La Liga in 12 attempts since joining
