Real Madrid won their 29th league title Photos from Real's win

Two goals from Ronaldo and one from fellow Brazilian Roberto Carlos gave Real the victory they needed.

Nearest rivals Real Sociedad beat Atletico Madrid 3-0 but had to settle for second place, two points adrift.

"We've got our reward after many tough months," said Real coach Vicente Del Bosque.

"Everybody at this club played a part in this triumph with their work."

Real's sporting director Jorge Valdano, the driving force behind David Beckham's signing, said: "We have suffered enormously over the course of the year and only after the third goal could we really relax.

"The league is always important and very difficult to win and that's why we are so delighted."

Deportivo La Coruna and Celta Vigo were already assured of finishing third and fourth and taking the remaining Champions League places, while last season's champions Valencia finished fifth to qualify for the Uefa Cup.

Barcelona's 2-0 home win against Celta pipped Athletic Bilbao to sixth and a Uefa Cup place.

WEEKEND RESULTS Saturday Rayo Vallecano 0-0 R Huelva CD Alaves 1-1 Valladolid Mallorca 1-0 Malaga Sevilla 0-3 Valencia Racing Santander 2-3 Osasuna D Coruna 2-1 Espanyol Sunday Villarreal 1-4 Real Betis Barcelona 2-0 Celta Vigo Real Madrid 3-1 Athletic Bilbao Real Sociedad 3-0 Atletico Madrid Latest La Liga statistics

In Saturday's games, Valencia stormed to a 3-0 win at Sevilla, while Rayo Vallecano and Recreativo de Huelva, both already relegated, shared a dull 0-0 encounter.

The result ensured that Rayo finish bottom and brought a disappointing end to their four-season spell in the top flight.

Recreativo, though, have the chance to bring their season to a happier conclusion when they face Real Mallorca in the final of the King's Cup next week.

The other relegated team, Alaves, could only manage a 1-1 draw at home to Valladolid, while Mallorca beat Malaga 1-0.

Deportivo La Coruna, already assured of third place, beat Espanyol 2-1, while Osasuna won 3-2 at Racing Santander.

Deportivo striker Roy Makaay scored his 29th goal of the season, and his 100th in Spain's first division, to help his side come from behind.

The Dutch international, who is the leading scorer in the Spanish first division, also laid on the winner for strike partner Albert Luque who fired home at the far post.

The game also marked what is likely to be veteran defender Donato's final appearance for the Galician club.

The 40-year-old centre back, whose contract with the club finishes at the end of the season, was treated to a standing ovation when he was replaced shortly before halftime.