The trade wasn't official yet but was confirmed to The Canadian Press by sources within both clubs.
The 27-year-old Tellqvist appeared in only one game with the Leafs this season, a 2-1 loss to New Jersey on Nov. 16. He was 16-16-2 with the Leafs for his career with a 3.01 goals-against average and .895 save percentage. He lost his backup job to J.S. Aubin late last season.
Nash, 31, has spent the season with San Antonio of the AHL where he had six goals and six assists in 19 games. Known throughout his career as an agitator, Nash has 64 points (27-37) and 673 penalty minutes in 374 career NHL games with St. Louis and Phoenix.
Also Tuesday, Maple Leafs defenceman Jay Harrison cleared NHL waivers and was assigned to the AHL's Toronto Marlies.
The 24-year-old appeared in five games with the Leafs this season, posting a minus-5 rating and six penalty minutes. He has one assist and eight penalty minutes in 13 career NHL games.