The 37-year-old man, who is in Egyptian custody, used a pretext for taking the children from their mother's home in Celle, Lower Saxony, on Easter Monday and flew with them to Egypt.
He is then said to have to taken the children – two boys aged six and eight and two girls aged four and five - to an undisclosed location in Sudan, before returning to Egypt.
The motive for the abduction appear to be the father's Christian-fundamentalist views, though more details will be disclosed at a press conference on Thursday. Early reports say the children are well and want to return to Germany.
The German Foreign Ministry cooperated with Egyptian authorities on the case, which caught the attention of TV programme "Aktenzeichen XY ungelöst "XY Files Unsolved" on state broadcaster ZDF in June. There were reports that the children had been seen in Bavaria.
The family's church, in the village of Hermannsburg, had called for donations and prayers for the children. Regina Keller, wife of pastor Wilfried Keller, said Wednesday that the congregation would be "ecstatic and thrilled" by the news. She said that in the past few weeks the mood had been sad as so little had been heard of the case.