One of them, Astrid Bouteuil, said on Friday she had never doubted he was her father and was "overjoyed" at the family link, saying the confirmation was "a great present" for her 43rd birthday on Saturday.
"It's proof that there's still a love story between 'old Europe' and 'new America'," she said from her home outside Paris.
She said she never doubted the identity of her father because Lindbergh had often visited his family at their then home in Munich, southern Germany. "But the story was never written."
The children's spokesman, Anton Schwenk, said the genetic tests supported their assertions about Lindbergh, who won instant celebrity after making the first solo, non-stop transatlantic flight in 1927.
Astrid Bouteuil and brothers Dyrk
(L) and David Hesshaimer
The probes, examined by a Munich university medical centre, compared their DNA with a sample from a member of Lindbergh's family.
The result showed a probability of paternity of more than 99%.
Bouteuil, now a mother of four, and brothers Dyrk and David Hesshaimer, 45 and 36 respectively, told the German Sueddeutsche Zeitung daily in August that they only learned their father's identity after his death in 1974.
According to them, quoting a clutch of letters he wrote, Lindbergh fell in love with 31-year-old Brigitte Hesshaimer, 24 years his junior, during a trip to Germany in 1957 and continued to see her until his death.
Pioneering pilot fell for a German
hat maker 24 years his junior
The children were born between 1958 and 1967. They were listed in official records as "father unknown," but they say he visited them often and supported them financially.
They said they only felt able to come forward after their mother died two years ago.
A book and a television documentary are currently in production in Germany about the affair.
Traditionally, Lindbergh has been portrayed as a happily married family man with five children. The claims that he fathered illegitimate children were met with deep scepticism in the United States.
Schwenk said the children had met in Europe with members of Lindbergh's US family since August.
"The establishment of family relations will grow naturally," he added. "The gap of so many years cannot be bridged in a few hours."
Bouteuil denied she had had any personal contact with Lindbergh relatives from the United States, but said a meeting was planned next summer. "To get to know his family is a dream," she added.
Also in August, the German news magazine Focus claimed that Lindbergh had another two illegitimate children in Germany - the fruits of a relationship with Hesshaimer's sister Marietta.
It said Marietta was now living in Switzerland in a house built for her by the aviator.