Murphy said he chose Boston because of its style of play.
"Watching both teams, I fit in better with the way Boston plays, the way they spread the floor, and you know I just like the way that they play," said Murphy, who had never reached the playoffs.
"That was the most important factor, going to a team that was going to not only be in the playoffs, but for a long playoff run. Looking at the teams, the Celtics have all the potential to do that."
The 6-foot-11, 245-pound former first-round pick from Notre Dame averaged 14.6 points and 10.2 rebounds last season with the Indiana Pacers. With the Nets, the New Jersey native averaged just 3.6 and 4.2 this season.
He played in just 18 games with New Jersey and hasn't played since Jan. 7. But he was in uniform for Wednesday night's game against Phoenix.
Murphy said he has been working out to stay in shape.
"I've never been really apart from a team for an extended period of time, so I couldn't really tell you," he said. "(It's) pretty crazy. I'm just looking forward to getting here and moving forward towards the future."
The Celtics have been one of the most active NBA teams in the past week.
At the trading deadline, they sent starting center Kendrick Perkins to the Oklahoma City Thunder along with Nate Robinson for forward Jeff Green and center Nenad Krstic. In a separate deal, Boston sent backups Luke Harangody and Semih Erden to Cleveland for a second-round draft pick.
Celtics general manager Danny Ainge said he wasn't done yet: He's hoping to add another shooting guard — perhaps as soon as Wednesday or Thursday.
"I'd like to bring in someone with some experience," he said. "I'd like to bring in someone that's not old and washed up."
Wednesday night's game was the first time in Boston for the rebuilt team.
"I know the crowd is going to be amazing, Green said before the game. "I've played here early in my career and it was great. So I'm looking forward to being part of it on the good side this time."
Celtics coach Doc Rivers said he is eager to get his team together in practice so he can get the new players familiar with the system.
"Since we're adding all these guys, the sooner we do it and put them all together, the better," Rivers said. "We're in the building phase, which we didn't think we would be in at this point in the year, but we are."