The Argentine, one of the world's best-paid players, and his father had been convicted of hiding image rights royalties in offshore accounts and had been given jail terms of 21 and 15 months respectively.
Following the ruling by Barcelona's provincial court, Messi will instead pay €252 000 and his father €180 000 in fines.
The fines correspond to €400 for each day the two men were sentenced to jail.
Under the original sentence, neither Messi or his father would have been likely to serve time behind bars, because in Spain first offenders for non-violent crimes are spared jail time for sentences of less than two years.
The two were in July 2016 found guilty of using companies in Belize, Britain, Switzerland and Uruguay to avoid paying €4.1 million in taxes on income Messi earned from his image rights from 2007-09.
The income relates to the five-time world player of the year's endorsement deals, including with Danone, Adidas, Pepsi-Cola, Procter & Gamble and the Kuwait Food Company.
The player and his father made a voluntary payment of five million euros - equal to the amount of the alleged unpaid taxes plus interest - in August 2013 after being formally investigated.
They were also fined around €3.5 million when they were convicted for tax fraud.
The Barcelona court said it took these payments into account when deciding to exchange their prison sentences for new fines.
"This made them both deserving of having the prison sentence substituted by a fine," the court said in a ruling released on Friday.
Spanish prosecutors last month said they did not oppose the changes to the sentences. They had asked during last year's trial for Messi to be absolved, arguing there was no evidence that the player was aware of how his income was managed.
During the trial, Messi had argued that he trusted his father with his finances and "knew nothing" about how his wealth was managed.
The court ruling caps off a golden week for Messi, who on Wednesday extended his contract with Barcelona until June 2021, just days after he married his childhood sweetheart in Argentina.
The club did not give financial details but club president Josep Maria Bartomeu said Messi was now the best-paid player in the world.
"He is the best player in the world and he is paid like the best in the world and in the history of football," Bartomeu said on Wednesday.
Prior to his contract extension, Messi was the world's third-highest paid sportsman with an income of $80 million, of which $53m was in salary and bonuses, according to a list published by Forbes magazine in June.
Messi is not the only footballer to run into problems with Spain's courts, with Real Madrid forward Cristiano Ronaldo the latest to have been summoned to appear before a judge investigating tax fraud.
He is due to be questioned on July 31 on suspicion of evading €14.7 million in taxes.
Brazil star and Barcelona forward Neymar and his parents are due to stand trial for alleged corruption over his transfer from Santos in 2013.
Barca's Argentine defender Javier Mascherano also agreed a one-year suspended sentence with authorities for tax fraud last year, while Manchester United manager Jose Mourinho was last month accused of committing tax fraud by Spanish prosecutors in 2011 and 2012, when he was in charge at Real Madrid.
And former Barcelona president Sandro Rosell was arrested in May in a money laundering investigation related to the sale of the Brazilian national team's television rights.