Leading striker Samuel Eto'o scored his 25th goal of the season to earn Frank Rijkaard's side a victory that left them with an unassailable 11-point lead over their rivals who have just two games left to play.
Barca, who have a game in hand, top the table on 79 points, Valencia have 68 from 36, two ahead of Real Madrid who visit struggling Racing Santander on Thursday.
Osasuna, who won 1-0 at Atletico Madrid, occupy the final Champions League place a point further behind Real and five ahead of Celta.
It is the Catalan club's 18th league title and they are the first team to successfully defend the crown since they won back-to-back titles in 1998 and 1999 under another Dutch coach Louis van Gaal.
Rijkaard's team have the chance to cap a brilliant season with a European triumph as they play Arsenal in the Champions League final in Paris on May 17.
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"Now we can approach the Champions League final with less tension. This team is making history."
BARCA CELEBRATIONS
Barcelona's players were told they had won the title as they left the pitch at halftime against Celta and the substitutes celebrated by throwing water over each other.
At the same time in Barcelona, fans of the club began to stream out on to the streets to celebrate the triumph.
The team emerged for the second half in the bizarre position of knowing they had won the title, yet with 45 minutes of their game left to play.
But in an impressive demonstration of the sort of motivation that has helped Barca dominate the Primera Liga for the past two seasons, Rijkaard's side managed to step up a gear and see off their rivals.
Suitably enough it was leading scorer Eto'o who grabbed the winner when he juggled the ball past two defenders and tucked it inside the post after a surging run by Mark van Bommel.
The Cameroon international was enveloped by all his team mates who bounced up and down in celebration of the goal and the league title.
Rijkaard then took the opportunity to replace Ronaldinho, Van Bommel and Giovanni van Bronckhorst and give Edmilson, Xavi and Silvinho a chance to share in the victory.
Celta's Jesus Perera hit the bar in the closing minutes and Barca keeper Victor Valdes had to make a great reflex save to deny the striker an equaliser just before the final whistle but the visitors held on to win.
VALENCIA DEFEAT
Valencia waved goodbye to their remote chances of depriving Barca of the title as they went down at relegation-threatened Mallorca.
Mallorca were rewarded for their ambitious approach when Venezuelan striker Juan Arango steered past Santiago Canizares after Victor burst through two defenders in the ninth minute.
Valencia recovered from the shaky start to equalise eight minutes later when midfielder Miguel Angel Angulo steered in from 12 metres after David Villa's neat cut back from the byline.
But Italian defender Cristiano Doni earned the islanders a vital win two minutes into the second half when he volleyed home on the turn after defender David Cortes clipped a pass into the area.
Alaves secured renewed hope of avoiding the drop with a 2-0 win over fellow strugglers Real Betis while Athletic Bilbao beat Real Zaragoza 1-0 at San Mames to ease their relegation worries.
Already-relegated Malaga, who lost 2-1 at Villarreal, bring up the rear with 24 points, Cadiz have 33 and Alaves 36.
Another six teams are within four points of the congested relegation zone.
