Financial terms of the deal, announced Tuesday, weren't revealed.
The 23-year-old Galiardi played only 35 games last season because of wrist and forearm injuries. He finished with seven goals and eight assists. The Avalanche selected Galiardi in the second round of the 2007 draft.
Rissmiller, 32, played for five teams last season, including the Lake Erie of the American Hockey League. He was originally signed by the San Jose Sharks in June 2003 and has played in 192 NHL games.
He is, in my opinion, one of the best defensemen in the NHL and continuing to grow. I think his game, from an offensive standpoint, he continues to drive our offense... I think there's still tremendous upside for Oliver.
— Coyotes GM Don Maloney on defenseman Oliver Ekman-Larsson