David Ali Sonboly, 18, who had a Glock pistol and more than 300 bullets, killed himself after the attack.
Bavarian government officials said he appeared to have bought the illegal pistol used in the attack on the so called "dark net".
Vigils continue in the city to commemorate the victims.
Seven of the dead were teenagers - two Turks, two Germans, a Hungarian, a Greek and a Kosovan.
A further 35 people were injured, but only four of them have bullet wounds.
The state government officials told a news conference that the victims of the attack had not been specifically targeted and were not classmates of the gunman.
Robert Heimberger, head of Bavaria's criminal police, said Sonboly had paid a visit last year to the town of Winnenden - the scene of a previous school shooting in 2009 - and took photographs.
Mr Heimberger added that the parents of the gunman remained in shock and were not able to be interviewed.
He said it was likely the Glock pistol Sonboly used - which had been reactivated - was bought on the "dark net" market, an area accessible only with the use of special software.
Sonboly was a keen player of "first-person shooter" video games, he said.
Mr Heimberger also said that police had not found the manifesto of Norwegian mass killer Anders Behring Breivik when they searched Sonboly's room at his parents' flat.
A day earlier, officials had raised the possibility of a link to Breivik, whose own attack was carried out five years earlier to the day.
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