The teams announced the swap of young defensemen Thursday. Borgman figures to play for the Blues' American Hockey League affiliate in San Antonio.
Borgman, 24, had 11 points in 48 games with the Maple Leafs in 2017-18. He spent last season with the AHL's Toronto Marlies.
Schmaltz, 25, has five assists in 42 NHL games with St. Louis. After playing 20 games with the Blues last season, he gives salary cap-strapped Toronto some cheap right-handed-shooting depth on the blue line.