Edmonton received a third-round pick in this year's draft and a fifth-rounder in 2015 from Ottawa for Hemsky, a pending unrestricted free agent who expected to be traded.
"After the summer (Oilers management) told me pretty much straight up they'd trade me, and I didn't get traded," Hemsky told reporters in Edmonton. "It comes to the end, it's a weird feeling and excited for the new challenge and play different hockey."
The Oilers got a fifth-rounder from Columbus in exchange for Schultz, a defenceman who is also set to be a free agent July 1.
Edmonton also lost defenceman Corey Potter on waivers, as he was claimed by the Boston Bruins.