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.
I kept refreshing the page on the NHL website after the second round and I was shocked he lasted that long. I'm sure the Coyotes were pretty happy to get him. He's such a good player and he plays big in big games.
— Arizona forward Henrik Samuelsson on prospect Edgars Kulda being drafted by the Coyotes