Argentine Messi, aged 29, was also fined €2m euros (£1.7m; $2.2m) by the court in Barcelona.
In addition to the prison term, Messi`s father, Jorge, was fined €1.5m for defrauding Spain of €4.1m in 2007-09.
However, neither man is expected to serve time in jail.
Under the Spanish legal system, prison terms of under two years can be served under probation.
The pair also face millions of euros in fines for using tax havens in Belize and Uruguay to conceal earnings from image rights.
`Corrective payment`
"The sentence is not correct and we are confident the appeal will show the defence was right," Messi`s lawyers said in a statement several hours after the guilty verdict was delivered.
The lawyers said that "there is a good chance that the appeal will succeed", adding that Messi had always acted in good faith.
The sentence can be appealed against via the Spanish supreme court.
The footballer and his father were found guilty of three counts of tax fraud.
As well as the jail terms, Messi and Jorge were also fined. They made a voluntary €5m "corrective payment", equal to the alleged unpaid tax plus interest, in August 2013.
Messi earns an estimated €36m per year at Barcelona, and his income of about €315m in the past decade has placed him 10th of Forbes magazine`s list of the highest-earning athletes in the world.
Lionel Messi: Barcelona star appeals over tax fraud verdict
07 July 2016
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Barcelona football star Lionel Messi and his father will appeal against a Spanish court decision to sentence them each to 21 months in jail for tax fraud, the player`s lawyers say.
