World Player of the Year Messi's deal has been extended by two years to June 30, 2018, which ties him until he is 31, the La Liga leaders said in a statement.
The 34-year-old Puyol, the club's captain, has agreed a three-year extension to June 30, 2016, which would effectively see the Spanish international through to the end of his playing career at 38.
Xavi's existing deal ran until June 2016 depending on appearances but the 32-year-old midfielder's new contract would now end then regardless of the number of times he played, Barca added.
The new contracts will be signed in the coming weeks.
"It is with great satisfaction that the board are able to bring continuity to this successful project with the renewed deals for Xavi, Puyol and Messi," Barcelona director Toni Freixa told a news conference.
"Puyol, Messi and Xavi are three basic pillars. It was essential to have our principal figures tied to the club.
"The buy-out clauses remain the same until there is a financial improvement."
Offering Messi a further two years indicates how important the Argentine is to the club and ensures they secure his services over the peak of his playing career, injury permitting.
At 25, Messi has already set a number of club scoring records and is favourite to win a fourth World Player of the Year award next month.
He has been the top scorer in the world's highest-profile club competition, the Champions League, for four years in a row, and hit the headlines recently as he racked up his 90th goal in 2012 for club and country.
'THE FLEA'
Barca built their team around the fleet-footed forward over four trophy-filled seasons under coach Pep Guardiola until he stepped aside last May, and the transition to former number two Tito Vilanova has failed to upset the 'the flea's' rhythm.
Messi has already scored 25 goals in 16 La Liga games this season, the latest being a double against second-placed Atletico Madrid in a 4-1 victory on Sunday which left Barca clear at the top, and 13 points ahead of their great title rivals Real Madrid.
Puyol has been a central figure at the heart of the Barca defence for more than a decade, famous for his commitment and aggression. His return after a string of injuries has settled a backline that looked distinctly shaky earlier in the campaign.
Speaking at a news conference on Monday, Puyol said: "I want to play until I am 40. I want to continue playing... but when it doesn't feel right I will stop whether I have a contract in place or not."
Like Puyol and Messi, playmaker Xavi is a product of the club's acclaimed youth academy, and has pulled the strings in midfield for more than a decade.
With Cesc Fabregas settling into the side more, and the talented Thiago Alcantara emerging, Spanish international Xavi has increased competition for his place but remains a vital part of Vilanova's plans.
