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The British team announced on Tuesday that Argentine F2 driver Franco Colapinto would replace Logan Sargeant for the remaining nine races of the season, starting with Sunday's Italian Grand Prix at Monza.
The suspects had threatened to publish the data on the dark web unless they received millions of euros, said prosecutors.
The two men from the western German city of Wuppertal were arrested on Wednesday and had been seeking millions of euros, Bild reported.
A family spokeswoman on Wednesday confirmed a Munich Labour Court judgement and settlement by Funke media group, publishers of the magazine Die Aktuelle, without making any further comment.
The latest edition of Die Aktuelle ran a front cover with a picture of a smiling Schumacher and the headline promising 'Michael Schumacher, the first interview'.
Justice K M Joseph headed a five-judge constitution bench that has asked for a law for terminally ill patients choosing to stop treatment.
Schumacher, whose Ferrari great father also raced for Mercedes from 2010-12, will attend every Grand Prix as back up for seven-time world champion Lewis Hamilton and George Russell.
Team boss Mattia Binotto told reporters that the 22-year-old German would be available to stand in at 11 of the record 23 scheduled races should Charles Leclerc or Carlos Sainz be unavailable.
The family have kept updates to a minimum since the accident and in an upcoming Netflix documentary, set to premiere on September 15, Corinna said privacy was very important to them.
"I wanted that MSC," the 21-year-old Haas driver told reporters during pre-season testing in Bahrain ahead of his F1 race debut there on March 28.
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