Barr was named Florida's associate coach, while Allen was named as an assistant coach. The two will join holdover assistant Mike Kelly and goaltending coach Robb Tallas.
Allen, who has been with the organziation the past three seasons, most recently served as head coach of the Portland Pirates after now-GM Tom Rowe was promoted from that spot to the Cats' front office.
Barr, who played 13 years in the NHL, spent last season as an assistant coach with the Buffalo Sabres.
In addition to the hires at the NHL level, the Panthers named Geordie Kinnear head coach of their unnamed AHL affiliate in Springfield to fill the vacancy created by Allen moving up the ranks.
Kinnear joins the organization after spending the last ten years as an assistant coach of the Carolina Hurricanes AHL teams, the Charlotte Checkers (2010-16) and Albany River Rats (2007-10).