The 21-year-old striker has put pen to paper on a five-and-a-half-year contract through to the summer of 2031.
The Championship outfit fought off strong competition from a host of European clubs to sign the highly-rated striker, who was leading goal scorer in Sweden’s Allsvenskan in 2025.
August who is son of Sparta Prague coach, Brian Priske, will strengthen Chris Davies’ options in attack and is Birmingham's fourth addition of the January transfer window.
Born in Denmark, Priske began his career with at FC Midtjylland and FC Copenhagen before taking in loan spells in the Netherlands.
Priske arrived at at Djurgardens IF in August 2024, and the following year he caught headlines in Sweden as he scored 18 league goals in 27 games to finish leading goalscorer in the Allsvenskan.
Priske also featured prominently in the UEFA Conference League as Djurgardens IF reached the semi-finals where they were eventually beaten by Chelsea.
At international level, he has represented Denmark at age-grade level as well as being capped six times for the Under-21 side.