Hartman and a 2018 fifth-round pick go to Nashville for a first-round and fourth-round picks in 2018 and prospect Victor Ejdsell -- a 22-year-old playing in Sweden.
"He's a young player, he's got a lot of grit, lot of sandpaper, good skill level and a playoff type of player," Predators coach Peter Laviolette said of Hartman, according to NHL.com. "He's somebody we feel can fit in with our group here.
"We know what the playoffs are all about. It's about playing the game fast and executing, but it's also about grit and determination and it becomes more physical and more competitive. I think those work to his strengths. He's still a skilled player ... but yet he's got a lot of determination the way he plays the game."
One year after scoring 19 goals in his first full season, Hartman -- like many Blackhawks -- took a step back. The 23-year-old had eight goals and 17 assists in 57 games and was a healthy scratch on a number of occasions.
Many thought last season that the Blackhawks had found the agitator that they lost when they traded Andrew Shaw to the Canadiens in June 2016, but Hartman struggled to find his way this season.
Hartman is scheduled to become a restricted free agent after the season.
After having the best record in the West during the regular season last year, the Blackhawks were swept by the Predators in the first round of the playoffs. Their struggles continued this year, with Chicago currently sitting 11 points out of the second wild card.
The Predators are first in the Central Division with 85 points after making a run to the Stanley Cup finals last year.