The 29-year-old has spent two and a half seasons in Bergamo, playing 92 matches and scoring 10 goals.
The move is initially a loan with the obligation to buy at the end of the season, Atalanta said in a statement.
Kurtic has been in Italy since January 2011, playing for Palermo, Varese, Sassuolo, Torino, Fiorentina and Atalanta.
SPAL are struggling just above the drop zone with Atalanta in seventh after pegging back AS Roma 2-1 before the winter break.
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