Officials initially blamed the E. coli, which has killed 29 people, on imported cucumbers, then bean sprouts.
In another development, Russia agreed to lift its ban on imports of EU fresh vegetables in return for guarantees.
The Russian ban had compounded a crisis for EU vegetable-growers, with Spanish cucumber producers wrongly blamed for the contamination.
Mr Burger, who heads the Robert Koch Institute, told reporters on Friday that even though no tests of the sprouts from a farm in Lower Saxony had come back positive, the epidemiological investigation of the pattern of the outbreak had produced enough evidence to draw the conclusion.
The institute, he added, was lifting its warning against eating cucumbers, tomatoes and lettuce, but keeping it in place for the sprouts.
Some 3,000 people have been taken ill with the German outbreak of E. coli, which involves a previously unknown strain of the bacterium.
Sufferers may develop haemolytic uraemic syndrome (HUS) where bacteria attack the kidneys and nervous system, giving them fits and often forcing them on to dialysis.
'Hot lead' "People who ate sprouts were nine times more likely to have bloody diarrhoea than those who did not," Mr Burger said.
Germany's top disease control official said the origin of the contamination was still believed to be the small organic farm in Lower Saxony which first came under suspicion at the weekend.
"The links are ever clearer - it's a hot lead," he told reporters in Berlin, at a joint news conference with the heads of Germany's federal institute for risk assessment and federal office for consumer protection.
He said it was possible that all tainted sprouts had now either been consumed or thrown away, but he warned the crisis was not yet over.
"There will be new cases coming up," he said.
Lower Saxony agriculture minister Gert Lindemann said earlier this week that experts had found no traces of the E. coli bacterium strain at the Bienenbuettel farm but he did not rule it out as the source of the contamination.
In an interview to be published in next week's edition of Focus magazine, Mr Lindemann said some 60 of the people taken ill had eaten sprouts from the farm, which employs about 15 people.
Contamination might have been caused by contaminated seeds or "poor hygiene", he added.
Ban to be lifted The agreement to lift the Russian ban was announced after talks between top EU officials including the Commission chief, Jose Manuel Barroso, and Russian counterparts in the central Russian city of Nizhny Novgorod.
- Wash fruit and vegetables before eating them
- Peel or cook fruit and vegetables
- Wash hands regularly to prevent person-to-person spread of E. coli strain
"We are ready to resume the shipments under guarantees of the EU authorities," President Dmitry Medvedev told reporters.Russia's top food safety officer, Gennady Onishchenko, said Russia would lift its prohibition after receiving food safety guarantees from the European Commission.
Mr Barroso said the EU would send a form for issuing food safety certificates to Russia in the next few days.
According to the Commission, the total value of EU exports of fresh vegetables to Russia is 600m euros (£530m; $870m) a year, a quarter of the total exported.
Spain, France, Germany and Poland are the biggest exporters.