The court in Barcelona found the Argentina player and his father, who handles his financial affairs, guilty of three offences.
Jorge Messi will also appeal against his 21-month prison term and fine of €1.5m (£1.28m).
He and his son, who is understood to earn £26m in annual salary under his current club contract alone and said to be worth at least £240m, were told they had the right to appeal.
Video:
Lionel Messi Arrives At Court
Messi, 29, told his trial he knew nothing of how his money was managed and admitted signing documents without reading them.
He said last month: "The truth is no, the truth is no, I didn't know.
"As my dad explained earlier I just dedicated myself to playing football, I put my trust in my father, in the lawyers who had decided to manage this thing."
Messi's lawyers said he had never examined contracts between 2007 and 2009 which dealt with income from image rights with companies including Adidas, Pepsi-Cola, Danone, Procter and Gamble, Banco Sabadell and the Kuwait Food Company.
But in its written judgment on Wednesday, the court said: "(His) avoidable ignorance, which was derived from indifference, is not an error, and it does not remove responsibility."
He made a voluntary payment of £3.8m in August 2013 to cover unpaid tax and interest. The sentencing - and appeal - should have no impact on his club career at Barcelona.
The club said: "FC Barcelona remains at the disposition of Leo Messi and his family to stand by him in any actions that he decides to take in defence of his honour and legitimate self-interests."
Messi - voted World Player of the Year five times - confirmed his international retirement in the run-up to the verdict after Argentina lost to Chile in the final of the Copa America.
Messi is Argentina's leading scorer with 55 goals in 113 international appearances.
With Barcelona he has won four Champions League titles and eight Spanish league titles, scoring 453 times in 531 games.
