As well as the suspended jail terms, the Argentina international was fined about €2m and his father €1.5m. They made a voluntary €5m "corrective payment", equal to the alleged unpaid tax plus interest, in August 2013.
Messi's appeal against the sentence was rejected by Spain's Supreme Court last month, but his father's jail time was reduced because he had paid some of the taxes.
The footballer was never expected to serve time in jail as under the Spanish system, prison terms of under two years can be served under probation.
Lionel Messi's highs and lows
Reached 500 goals for Barcelona in April 2017
Winner of Fifa Ballon d'Or as world's best footballer on five occasions - a record
Voted Uefa best player in Europe three times
Uefa Champions League winner with FC Barcelona on four occasions
Spanish championship winner with FC Barcelona eight times
Holds the record for most goals in Spain's La Liga
Olympic gold medallist with Argentina in 2008
Argentina's all-time leading scorer with 55 goals
...and major disappointments:
16 June 2016: Quits Argentina team after missing penalty in shootout in Copa America final loss to Chile (he later reversed the decision)
it was the fourth major final defeat for Argentina in nine years
other three losses: Copa America (2015) again to Chile (again on penalties); 2014 World Cup to Germany; Copa America (2007) against Brazil