Anders Hoegstroem, a former neo-Nazi leader, admitted theft under a plea bargain last month and will be moved to Sweden to serve his sentence.
The infamous sign was stolen in December last year and recovered in three pieces three days later.
The judge in Krakow also jailed two Poles for up to two-and-a-half years.
One of the pair, named as Andrzej S, apologised in court for the offence, Polish media report.
The 5m (16ft) wrought-iron slogan which translates as "Work sets you free" is a potent symbol of many of the Nazi-era atrocities. During the Nazi Holocaust, 1.1 million people - most of them Jews - were murdered at Auschwitz.
The sign has since been repaired although it now hangs in the Auschwitz museum and has been replaced by a replica at the entrance to the former death camp.
Three other Poles were given prison terms earlier this year for the theft which was thought to have been ordered by another Swede still at large. So far, no evidence of other individuals has come to light.
Hoegstroem, 34, who was detained in Sweden in February had at first denied involvement in stealing the sign but later changed his plea.
On being told the verdict, he said he accepted the court's decision. He is now likely to be returned to Sweden in a week's time.
BBC News
