Goaltender Mike Condon is heading to Florida along with a 2020 sixth-round draft pick, while Ottawa also receives Tampa Bay's fifth-round pick for next year.
Callahan, 34, was placed on long-term injured reserve in June after he was diagnosed with a degenerative disk disease of his lumbar spine. Doctors recommended that he no longer play hockey.
Tampa Bay gets salary cap relief as they work on re-signing restricted free agent forward Brayden Point. The 23-year-old had career highs with 41 goals and 51 assist last season.
"We believe we have the right mix of goaltenders both for the upcoming season and the future," Ottawa general manager Pierre Dorion said. "We are pleased with how our young goaltenders have been developing in Belleville, so this trade allows us to focus on continuing their growth at a proper pace while keeping two established goaltenders here in Ottawa."
Callahan is under contract through next season and is a $5.8 million cap hit.
"Our cap flexibility allowed us to proceed with this trade, which will also benefit us as we continue making adjustments to create a hardworking, exciting team," Dorion said.
Callahan came up with the New York Rangers in 2006 and was traded to Tampa Bay in the 2013-14 season. In 13 seasons he scored 186 goals with 200 assists.
Condon, 29, joins the Lightning one day after they signed goalie Andrei Vasilevskiy to an eight-year extension worth $76 million.
The extension begins with the 2020-21 season and keeps Vasilevskiy with the team through the 2027-28 season.
Condon has played in 129 games over four seasons with Pittsburgh, Montreal and Ottawa, with a 45-58-17 record and a 2.79 goals-against average.
The addition of Condon means Tampa Bay currently has six goalies on their roster. Besides Vasilevskiy, the Lightning also have Louis Domingue, Spencer Martin, Curtis McElhinney and Scott Wedgewood on their roster.