Sanchez, who recently left Arsenal to join Manchester United, reached an agreement with the Spanish Attorney General to pay back the tax he failed to pay, a sum of just under £900,000, plus a fine of £525,000.
He was also handed the jail sentence but will not have to spend any time in prison unless he commits a similar offence within the next two years.
Sanchez joined Barcelona in July 2011 and played nearly 150 games for the club before leaving for the Premier League three years later.
He was accused of defrauding the Spanish Treasury of 1m euros between 2012 and 2013, relating to income from his image rights.
The Chilean is the latest in a long line of football stars to be pursued by Spanish tax authorities over their image rights, with Lionel Messi, Cristiano Ronaldo, Jose Mourinho and Ricardo Carvalho all being investigated.
Messi was handed a 21-month jail term in 2016 but saw that reduced to a fine as Spanish law means first-time offenders sentenced to less than two years in jail do not serve any jail time.