Högström, 34, arrived in Warsaw aboard a Polish military aircraft, after which he was transferred by helicopter to Krakow where prosecutors are investigating the case, police said.
Högström was arrested on February 11 over the theft of the "Arbeit Macht Frei" sign from the gate of the notorious World War II death camp set up in Poland by Nazi Germany. The theft was carried out on December 18.
On March 11, a Stockholm court allowed his extradition to Poland to face trial.
Högström in 1994 founded the National Socialist Front, a Swedish neo-Nazi movement he headed for five years before quitting.
He has told Swedish media he was to act as an intermediary to pick up the sign and sell it to a buyer, but claimed that he informed Polish police about the people behind the plot.
Polish police recovered the five-metre (16-foot) metal sign, whose German inscription means "Work Will Set You Free", on December 20. They arrested and charged five Polish men.
The sign, which had been cut into three parts, was returned by investigators to the Auschwitz museum on January 21, less than a week before commemorations for the 65th anniversary of the camp's liberation by Soviet troops.
The sign has long symbolised the horror of the camp where some 1.1 million people -- one million of them Jews -- were victims of Nazi German genocide from 1940 to 1945.
Polish judicial authorities indicted Högström in January and issued an arrest warrant for him on February 2.