Nate Robinson will be going to Boston, though it is expected to be a temporary stay as he is expected to seek a buyout of his contract with the intention of signing with a playoff team.
Robinson, who is coming back from an ACL tear, is averaging a career-low 5.8 points on a career-low 35 percent shooting in 33 games for the Nuggets.
Nelson played in just six games for the Celtics and is averaging a career low 6.8 points on a career-low 34 percent shooting in 29 games with the Dallas Mavericks and Celtics.
He has a player option in his contract for next season for $2.8 million.
This is the second trade the Nuggets have executed in the last week as they begin to retool their roster. The Nuggets are involved in trade talks for other players including Arron Afflalo and Randy Foye, according to sources.
Yahoo! Sports earlier reported the trade.