The authorities said the man, a 42-year-old identified only as Holger B., had given himself up on Tuesday at a court in Palma and had been remanded in custody by a magistrate.
"We had early indications that the suspect had fled to Majorca," said Hannover police spokesman Heiko Steiner.
An argument in a bar early on Monday, apparently about the performances of Italy and Germany in past football World Cups, turned deadly when B. left the pub, returned a short time later with a 9mm pistol and shot the two Italians in the head, according to German police. Both the victims, aged 47 and 49, died later.
Majorca is a favourite spot for Germans, with nearly four million visiting the Mediterranean island annually and tens of thousands living there permanently.
"We have no doubt the suspect will quickly be extradited to Germany," said Irene Silinger, spokeswoman for Hannover's state prosecutor's office.
The atmosphere was expected to be febrile later Wednesday with Spain playing Germany in the World Cup semi-finals. Italy, one of the favourites after winning the 2006 World Cup, crashed out in the group stages after a humiliating loss to Slovakia.