The 27-year-old, who scored against Germany in a recent World Cup qualifier, makes the move for an undisclosed fee in the summer having appeared 18 times in the top flight this season.
"I had really good talks with the club bosses who were able to convince me of their concept, regardless of what league they will be playing in," said Schmidtgal.
"They really made an effort for me, even if I have not had the best of second halves of the season due to injury.
"I am convinced Fortuna will stay up."
With Furth's relegation already secured, Schmidtgal has not necessarily retained his place in the top flight by moving to Fortuna.
With two games of the season remaining, they are level on points with Augsburg, who are in the relegation play-off berth, and could yet follow Furth down into the second division.