The Flames received a second-round draft pick this June plus a fourth-round pick in 2018 for Hudler. The Oilers got a third-round pick for Purcell.
Hudler, a pending unrestricted free agent, has 10 goals and 25 assists this season for the Flames.
Drafted in 2002, Hudler, 32, played his first seven seasons with the Detroit Red Wings before heading to Calgary as a free agent in 2012.
Purcell has 11 goals and 21 assists in his second season with the Oilers. A 30-year-old forward, he also has played for the Kings and Lightning.
The Panthers also announced they acquired veteran defenseman Jakub Kindl in a deal with the Red Wings for a sixth-round pick in the 2017 draft. Detroit will retain 15 percent of Kindl's salary, a source told ESPN The Magazine's Craig Custance.
In trading Kindl, the Red Wings clear valuable cap space, most notably for next season. They will retain $360,000 of his salary, with Florida picking up about $2 million in cap space this season and next.
The Panthers' flurry of moves come as they prepare for what would be the franchise's first playoff appearance since the 2011-12 season. Florida entered play Saturday with a three-point lead in the Atlantic Division and sitting second overall in the Eastern Conference.
Information from ESPN The Magazine's Craig Custance contributed to this report.