Bayern Munich completed the German double with a Cup final win over Borussia Dortmund, and in the Bundesliga, all eyes were on three-times champions Hamburg who retained their top-flight status after edging out second-tier Gruether Fuerth in a two-legged play-off.
Alexis Sanchez gave Barca hope when he scored from a narrow angle in the 33rd minute but Diego Godin's header from a corner was enough for Atletico, who finished on 90 points from 38 matches, three ahead of Barca.
Real Madrid, who beat Espanyol 3-1 at the Bernabeu on Saturday, also finished on 87 points but lost home and away to Barca, meaning the Catalan club had a superior head to head record and finished ahead of their arch-rivals.
Osasuna and Real Valladolid were unable to avoid the drop on Sunday and will join Real Betis in the second division next season.
Germany when they beat rivals Borussia Dortmund 2-0 with two extra-time goals to win the German Cup and secure a 10th domestic double.
Dutchman Arjen Robben, who scored the winner against Dortmund in the Champions League final last season, and Thomas Mueller grabbed the goals.
Hamburg retained their Bundesliga status by seeing off second-tier Gruether Fuerth in a playoff. They remain the only team never to have been relegated since the Bundesliga was created in 1963.
Juventus, who won all 19 home matches, completed their campaign with 102 points after winning 33, drawing three and losing two of their 38 games. They finished 17 points clear of AS Roma, who lost 1-0 at Genoa.
In the only outstanding matter to be settled on Sunday, Parma beat relegated Livorno 2-0 to snatch sixth place and the final Europa League spot.
AC Milan, who finished one point behind in eighth, missed out on European football despite beating Sassuolo 2-1.
Benfica, beaten on penalties by Sevilla in Wednesday's Europa League final after a 0-0 draw, had already won the league and the League Cup.
The result put Lille, who will play in the third qualifying round of Europe's elite club competition, on 71 points, two ahead of St Etienne, who won 3-1 at home to AC Ajaccio.
Paris St Germain, already crowned champions, celebrated a second consecutive title with a 4-0 home victory over Montpellier.
Anderlecht were crowned Belgian champions for the 33rd time after a 3-1 victory over Lokeren was sufficient to pip rivals Standard Liege to the title on the final day of the season.
Anderlecht, who qualified for next season's Champions League group stage, finished the 10-game playoffs - which pits the six most successful teams from the regular competition - two points ahead of Standard who beat Racing Genk 1-0 at home.
For the first time in 12 years the Dutch top flight will have three new clubs next season after Willem II Tilburg won automatic promotion and were joined by Dordrecht and Excelsior who went up via the playoffs.
Dordrecht return to the top flight for the first time in 19 years after beating Sparta Rotterdam.
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