Each player was given a one-year, two-way contract.
Desjardins, 27, appeared in three games with the Lightning in 2012-13, with a record of 0-3-0, a 3.00 goals-against average and .890 save percentage.
He played in 36 games in the American Hockey League, split between the Hamilton Bulldogs and Syracuse Crunch, registering a record of 15-18-3 to go with a 2.61 goals-against average and .910 save percentage. He appeared in 18 Calder Cup playoff games with Syracuse, posting a record of 13-5-0 to go along with a 2.30 goals-against average and .908 save percentage. Syracuse lost in the finals to Grand Rapids.
Taormina, 26, skated in two games with Tampa Bay last season and was scoreless. He also skated in 55 games with the Crunch, collecting four goals, 24 points, 21 penalty minutes and a plus-10 rating.
He has appeared in 49 NHL games with the New Jersey Devils and Lightning. He was signed by Tampa Bay as a free agent on July 6, 2012.