Schreiber, who has served as the Federation's executive director for the past two years and has over 25 years experience as a professional staff member, was voted in unanimously by the ISSF's Administrative Council.
He takes office with immediate effect.
President Olegario Vázquez Raña said: "The ISSF is very fortunate to have someone available who is so well prepared to serve as its secretary general.
"Franz is a young man who is hardworking, honest, loyal and absolutely dedicated to the ISSF.
"For the last two years he has been deeply involved in doing the work of the secretary general and his work has been outstanding.
"Our National Federation leaders and our athletes and coaches already know Franz well."
Schreiber, who is 49, began his professional career as a legal intern in 1982 and became a full-time employee at ISSF two years later.
"I am very happy about the great trust that I have been given," he said.
"I will continue to work for the ISSF and the shooting sport with all my heart and my full energy.
"I look forward to supporting President Vazquez Raña and the ISSF to further strengthen the shooting sport in my new capacity as secretary general."
December 2010: Tributes as head of ISSF dies in Munich