The teams announced the swap of AHL players Tuesday night.
Klimchuk was selected 28th overall by the Flames in the 2013 NHL Draft but has played just one regular-season NHL game to date. The 23-year-old has three goals and five assists in 16 games this season with the Stockton Heat in the AHL where he has spent the past four seasons. Klimchuk has 44 goals and 56 assists throughout his 204-game AHL career.
Nielsen, a third-round selection of the Maple Leafs in 2015, is heading back to his home province after spending the past three years in Ontario. The 22-year-old is from Red Deer, Alta., and spent his entire junior career with the WHL’s Lethbridge Hurricanes. Nielsen has 20 goals and 50 assists in 152 career AHL games, all spent with the Toronto Marlies.