The trio were given jail sentences ranging up to two-and-a-half years.
The court in Krakow said the men had admitted the theft, and so the case did not have to go to trial.
Two other Poles remain in custody over the theft of the 5m (16ft) wrought-iron sign, which was quickly recovered and found cut into three pieces.
The authorities in Stockholm said last week that a Swedish former neo-Nazi accused of instigating the theft will be extradited to Poland to face trial.
The sign had been half-unscrewed, half-torn from above the memorial site's gate.
A replica sits on top of the entrance, while the original is being repaired.
The sign - the words on which translate as "Work sets you free" - symbolises for many the atrocities of Nazi Germany.
Its theft caused outrage in Israel, Poland and around the world.
More than a million people - 90% of them Jews - were murdered by the Nazis at Auschwitz in occupied Poland during World War II.
BBC News
