The scientists compared the DNA obtained from a piece of the skull with a tissue sample donated by an 83-year-old relative of Bormann's living near Frankfurt and found matching sequences.
Coupled with eyewitness testimony and dental records, the German authorities are convinced their file on one of the most notorious war criminals can be closed.
Contrary to legend, Hitler's deputy died in all probability on 2 May 1945.
The man spotted in Paraguay, Spain, Italy and Russia in the last five decades must have been an impostor or, more likely, the figment of fiction- writers' imagination.
The Bormann myth began in the dying days of the Third Reich. The Nazi party leader and Hitler's private secretary was entrusted with the Fuhrer's testament and, conceivably, vast sums of money. On 2 May 1945 he left the bunker on a mission to take Hitler's orders to Admiral Karl Donitz, the Fuhrer's nominated successor. He promptly disappeared.
According to one theory, he managed to escape from Berlin and was smuggled to South America on board a U-boat. Over the years, there have been persistent sightings in Paraguay and Brazil.
The official version accepted Bormann as dead, though the Allies took the precaution of sentencing him to death in abstentia in Nuremburg.
One leading Nazi testified seeing him outside the bunker on 2 May, in the company of Hitler's doctor, Ludwig Stumfegger. Bormann and Stumfegger came across Soviet troops as they were fleeing, and took their lives by swallowing cyanide capsules.
The testimony had one weakness. In 1965 the West Berlin authorities dug up the ground at the spot where the two bodies were allegedly lying and found nothing. The powerful Bormann myth, nurtured by neo-Nazis, was rekindled. Bormann apparitions flooded in from every corner of the globe, forcing German investigators on a wild-goose chase from Patagonia to the Amazon jungle, and back to southern Europe. More than 6,000 sightings have been reported; dozens of aliases had to be checked out.
The Germans had to dig again. In 1972, a derelict site near the Reichstag revealed the two skeletons close to the place where the original witness had placed them. One had belonged to an extremely tall man - Stumfegger - while the other matched Bormann's features.
Since then the remains have been in the possession of prosecutors in Frankfurt awaiting yesterday's final proof. "It is painful for us," wrote Martin Bormann, the 68-year old son of the mass murderer, "that nothing has been known for certain about our father since 2 May 1945."
Mr Bormann, a priest who never misses an opportunity to speak out about his father's crimes, now plans a secret funeral. So as not to create a Nazi-shrine, the remains are expected to be cremated and scattered in the wilderness, possibly at sea.