Brule was playing for Edmonton's American Hockey League affiliate in Oklahoma City and needed to clear waivers before returning to the NHL after the Oilers tried to recall him. The Coyotes, instead, claimed him.
The 25-year-old Brule had eight goals and 10 assists for 18 points in 27 games for the Barons this season. He appeared in 41 games for the Oilers last season and compiled seven goals with two assists for nine points.
Columbus selected Brule with the sixth overall pick of the 2005 NHL Entry Draft, but he never lived up the lofty expectations and was traded to Edmonton in the summer of 2008 for Raffi Torres.
Brule has recorded 38 goals and 43 assists for 81 points in 263 NHL games with the Blue Jackets and Oilers. His best season was 2009-10, when he tallied career bests of 17 goals and 20 assists in 65 games for Edmonton.
Phoenix also activated center Boyd Gordon off injured reserve on Tuesday. He had missed seven games with a lower body injury.