The 31-year-old woman is suspected by police in Sweden of the murder on March 17 of two children, 1 and 3, and the attempted murder of their 23-year-old mother.
German authorities are planning to send the suspect to Sweden next week.
"But for security reasons we do not want to say what day or reveal any other details about the surrender," said Jörg Fröhlich from the prosecutor's office in Celle in northern Germany.
The suspect can choose to appeal the decision all the way to Germany's Constitutional Court in Karlsruhe.
"It is her last chance to appeal the surrender. The Constitutional Court will make a quick decision. It will probably only take a few days," said Fröhlich.
The murdered children's 23-year-old mother was seriously injured in the attack and is still receiving hospital treatment. The children's father was arrested shortly after the incident but was quickly cleared of any involvement.
The 31-year-old suspect was previously romantically involved with the 23-year-old's current boyfriend.