Nash had been "reassigned" to the San Antonio Rampage and DeSantis to the Hamilton Bulldogs last week. The trade made the move official.
The 26-year old DeSantis had three goals and eight assists in 32 AHL games this season. The five-foot-11 rearguard from Oxford, Mich. has 16 goals and 65 assists in 183 career AHL contests.
Nash, 25, signed with Montreal as a free agent out of Cornell University in 2010. Mainly a power-play point man, the Kamloops, B.C., native played two NHL games in 2010-11.
He missed all of last season with a shoulder injury. Nash had a goal and seven assists in 26 AHL games this season.