The chase involving several police vehicles came to an end when the 66-year-old had an accident on the motorway close to the Catalan community of Jafre some 40 kilometres south of the border with France, police said.
Police said no-one was seriously injured in the accident and investigations have begun, with the driver due to appear before a judge on Friday.
According to Spanish newspaper El Pais, the incident began on Thursday afternoon at the French-Spanish border, when the man suddenly turned his car around at a checkpoint in French Le Boulou and drove away in the wrong direction.
French police immediately contacted Spanish authorities.
Spanish citizen in Switzerland
The man was a Spanish citizen who had long lived in Switzerland, El Pais reported, citing the authorities.
The dead passenger was reportedly his Swiss life partner, a man who had died at the age of 88 in unclear circumstances around three weeks earlier. An autopsy will be carried out, the paper said.
It is thought that the man wanted to drive to his deceased partner's corpse home to Switzerland.
Because of the coronavirus pandemic there are currently border controls between Spain and France at which travellers must present negative PCR test results.