D'Agostini scored a career high 21 goals and 25 assists in 2010-11 but has been a victim of the numbers game in recent times due to the depth at forward in St. Louis.
The 25-year-old Sault Ste. Marie, Ont., native has appeared in just 16 games this season, with a goal and an assist.
D'Agostini was originally selected by Montreal in the sixth round of the 2005 draft and has compiled 45 goals and 46 assists in 254 NHL regular season games with the Blues and Canadiens, to go along with 115 penalty minutes.
New Jersey also gets a seventh round pick in the 2015 draft, with St. Louis earning a fourth- or -fifth-round choice in the same year's draft.