The 29-year-old Horton has not played this year due to a back injury.
Clarkson missed two games this month as a healthy scratch and has recorded 10 goals and five assists in 58
"He showed flashes, there were some moments where we had the David that we hoped to have, but overall I think it was probably disappointing for both sides," Toronto general manager Dave Nonis said in a press conference before Thursday's game against the Flyers.
Horton was signed as a free agent by Columbus on July 5, 2013. He missed the majority of the 2013-14 season, playing only 36 games, due to shoulder surgery and may be out long-term. He last played on Jan 2, 2014.
"We get a player back where if he ever came back he's an elite player, and in the event he can't we've created some cap space," Nonis said.
More of Nonis' comments about the trade were tweeted by the Leafs.
"This fell together. It worked for both sides. Once we started discussing it, we found it made sense. For David, we wanted him to get to his new team and get playing. Its available cap space and we can take advantage if Nathan is unable to play," Nonis said.
Horton's contract with the Blue Jackets is a seven-year, $37.1 million US deal very similar to Clarkson's contract with the Leafs. Clarkson signed a 7 year, $36.75 million US contract in 2013 leaving five seasons left on the deal. Both contracts are due to expire after the 2019-20 season.
"David Clarkson has been a 30-goal scorer in the NHL who will bring added character and leadership to our group and we believe he will be a valuable contributor to our team," Blue Jackets general manager Jarmo Kekalainen said in a statement.
"While we are excited to welcome David to the Blue Jackets, it is also difficult that Nathan's time here has ended prematurely due to his injury situation. He is a tremendous person and we wish him and his family all the best in the future," Kekalainen said.
Horton has played in 627 career NHL regular season games for teams including Columbus, Boston and Florida, recording 421 points.
Horton has also played in 43 playoff games, earning 36 points and winning a Stanley Cup with the Bruins in 2011.