Pirri is expected to join the Panthers on the road in Boston for Tuesday night's contest against the Bruins.
"Brandon is a young and talented player who we are extremely pleased to have acquired," Tallon said in a statement. "He has experienced tremendous success on the American Hockey League level, being named MVP of the All-Star game and winning the league's scoring title. Pirri further adds to our depth at center along with Aleksander Barkov, Nick Bjugstad and Drew Shore. We look forward to his contributions to our team."
The 22-year-old Pirri rounds out a core of young two-way centers Tallon has been building through the system. Scouts regard Pirri as a strong puckhandler and playmaker with the potential to be a top-six center.
Pirri, Chicago's second-round (59th overall) choice in 2009, was part of the last draft class of Tallon's tenure with the Blackhawks. Pirri is the second prospect this season -- the other being defenseman Dylan Olsen -- previously drafted by Tallon in Chicago now headed to Florida.
Despite having led the the American Hockey League in scoring last season with 22 goals and 53 assists in 76 games with Rockford, Pirri was unable to become a regular in Chicago's lineup.
He split this season with Chicago (28 games) and Rockford (26 games). The Blackhawks' recent acquisition of center Peter Regin dropped him further on the depth chart.
At the NHL level, Pirri has registered six goals and seven assists in 35 contests dating back to 2010.
With Rockford this season, he has 11 goals and 15 assists in 26 contests. Pirri represented Rockford at the AHL All-Star Game and captured MVP honors with two goals and an assist.
In a separate, minor-leauge deal earlier in the day, Florida acquired winger Mark Mancari from the St. Louis Blues for winger Eric Selleck.