Barca did not publish details of the deal but Spanish media said Messi, 26, would remain tied to the club until June 2018, as in his previous contract, and could earn around 5 million euros more per season in performance-linked bonuses.
The Argentina captain would also regain control of his image rights, one report said, further boosting the income of a man Forbes magazine estimates is the 10th highest-earning athlete, with annual revenues of $41.2 million including wages and endorsements.
"FC Barcelona has reached an agreement to adjust the terms in the contract binding Leo Messi to the club as a professional first team player," Barca said in a brief statement on Friday.
"The revised and updated contract will be signed over the next few days," they added.
Messi, who had been earning a net 13 million euros per season, will top soccer's earnings list ahead of Real Madrid forward Cristiano Ronaldo on 18 million euros and Zlatan Ibrahimovic of Paris St Germain on 14.7 million, sports daily Marca said.
Messi is Barca's all-time leading scorer with 354 goals in 424 official games and news of the deal is a boost for the club before Saturday's La Liga showdown against Atletico Madrid.
"Anything that is good for Messi is good for Barca," coach Gerardo Martino told a news conference on Friday. "It is a very good piece of news for both parties."
Since Messi made his debut in the 2004-05 season, Barca have won 21 titles, including three Champions Leagues and six La Liga crowns.
He joined Barca's academy at the age of 13 after a spell at Newell's Old Boys in his native Rosario.
Messi and his father last year paid 5 million euros to the Spanish authorities as a "corrective payment" after they were accused of filing false tax returns.
The pair, who both denied wrongdoing, allegedly hid more than 4 million euros by filing incomplete returns for the years 2006 to 2009.
The sale of Messi's image rights had been hidden using a complex web of shell companies in Uruguay, Belize, Switzerland and the United Kingdom, the prosecutor's office for tax crimes in Catalonia said.