Interior Minister Thomas de Maiziere said the teenager had likely hacked a girl's Facebook account and used it to lure victims to the McDonald's outlet where he began his rampage.
"There is absolutely no link to the Islamic State," Munich police chief Hubertus Andrae said, with prosecutors describing the assault as a "classic act by a deranged person".
Investigators see an "obvious link" between Friday's killings and Breivik's massacre of 77 people in Norway exactly five years earlier, Andrae added.
Chancellor Angela Merkel, in her first reaction to the carnage, said Munich had suffered a "night of horror".
Most of the victims in Friday's attack were young people, with three aged just 14, police said.
Munich prosecutor Thomas Steinkraus-Koch said Sonboly had suffered depression, but voiced caution over reports he may have undergone psychiatric treatment.
The teenager had 300 rounds of ammunition in a rucksack when he targeted the busy Olympia shopping mall, just minutes away from the flat he shared with his family, according to authorities.
Police are investigating how he managed to obtain his weapon, a 9mm Glock pistol with a defaced serial number.
- Tributes for victims -
Grieving Munich residents laid roses and lit candles in memory of the victims, with one placard bearing the simple plea: "Why?"
"Bloodbath in Munich," was the headline on the best-selling Bild newspaper.
Sixteen people were wounded in the attack, three of them critically.
A video posted on social media appeared to show a man in black walking away from the McDonald's restaurant while firing repeatedly with a handgun as people fled screaming.
A police patrol shot and wounded Sonboly but he escaped before police found his body, after an operation to track down what had initially been thought to be up to three attackers.
- Terrifying scenes -
Neighbours said Sonboly was born to Iranian parents, a taxi driver father and a mother who worked at a department store. They arrived in Germany as asylum seekers in the late 1990s.
Of Shiite Muslim origin, Sonboly appears to have converted to Christianity, hence his first name David.
The family lived in the well-heeled Maxvorstadt neighbourhood in a tidy social housing block popular with immigrant families.
Neighbour Delfye Dalbi, 40, described Sonboly as a helpful young man who was "never bitter or angry", though others remembered a quiet loner.
"All his body language said 'I don't want to talk to you,'" said Stephan, a waiter at the cafe on the ground floor of the housing block.
A police source cited by DPA news agency said he loved playing violent video games and was an admirer of the 17-year-old German who shot dead 15 people at his school near Stuttgart in 2009.
Andrae of the Munich police said the teenager had been obsessed with books and articles about mass killings "linked to maniacs".
Survivors described terrifying scenes Friday as shoppers rushed from the area, some carrying children in their arms.
"We entered McDonald's to eat... then there was panic, and people ran out," one woman told Bavarian television.
Another video appeared to show the gunman on a car park roof in a heated exchange with a man on a nearby balcony.
"I'm German, I was born here," the assailant replied after the man fired off a volley of swear words, including an insulting term for foreigners.
- Victims lured -
De Maiziere told reporters that Sonboly had likely used a hacked Facebook account to lure people to the McDonald's branch, "offering them special reductions".
"I will give you whatever you want, for not a lot of money," the online invite read, according to German media reports.
The casualties were mostly young, with three aged just 14 and two aged 15.
Most of the victims in Friday's attack were foreigners, including three Turkish nationals, three people from Kosovo and a Greek.
- 'Europe stands united' -
US President Barack Obama voiced staunch support for Washington's close ally Germany, while EU foreign policy chief Federica Mogherini said: "Europe stands united."
Europe has been on high alert for terrorism after a string of attacks in neighbouring France and Belgium claimed by IS.
The attack came just four days after a 17-year-old asylum seeker went on a rampage with an axe and a knife on a train in Bavaria, injuring five people.
In France, a Tunisian used a truck on July 14 to mow down 84 people after a Bastille Day fireworks display in Nice, the third major attack on French soil in the past 18 months.
Friday's massacre spurred many in Munich to think the unthinkable.
"It has reached us. People in Munich have long had a queasy feeling. Fears grew with every attack in Paris, Istanbul or Brussels," said the Abendzeitung newspaper's editor-in-chief Michael Schilling.
"Since Friday it is clear that there can be no security anywhere, not even in the safest German city."