The prison sentences are likely to be suspended as is common in Spain for first offences for non-violent crimes carrying a sentence of less than two years.
The Argentine's lawyers feel an appeal would eventually succeed in persuading the court that Messi and his father have behaved correctly, the player's representatives told AFP in a statement.
The Barcelona court found the Argentina international and his father Jorge Horacio Messi guilty of using companies in Belize, Britain, Switzerland and Uruguay to avoid paying taxes on 4.16 million euros of Messi's income earned from his image rights from 2007-09.
The court found Messi and his father, who has managed his son's affairs since he was a child, guilty of tax fraud and ruled that for each of those three years they should serve a sentence of seven months.
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Messi, 29, a five-time world player of the year winner, was also fined 2.09 million euros while his father was fined 1.6 million euros.
They can appeal the decision to Spain's Supreme Court and that is what the pair's lawyers indicated today they would, saying they felt confident an appeal would succeed.
Prosecutors had asked for Messi to be absolved, arguing there was no evidence that the player was aware of how his income was managed.
The state attorney representing tax authorities in the trial, Mario Maza, said he found it unlikely that Messi knew nothing about the situation.
"There is no deliberate ignorance here, it's fraud and that's all there is to it, because he didn't want to pay his taxes," he said.
The court agreed, arguing in its ruling that Messi "had decided to remain in ignorance".
"Despite all the opportunities available to the player to show interest in how his rights were managed, he did not," the court added.
The court said if the player was not punished, "ordinary" citizens could conclude that it was better to "not show interest" in their tax obligations.