The D-backs acquired the right-hander in exchange for cash considerations, but ultimately he was the player to be named later in the Jon Rauch trade.
Being dealt was nothing new for Mulvey, who was traded from the Mets to the Twins as part of the Johan Santana deal after the 2007 season.
"This is definitely more exciting now, because I went right to the big leagues," Mulvey said. "Here I am in Los Angeles, in Dodger Stadium. I think it's a great opportunity. Now it's up to me to just work hard and hope for success and do everything that I can."
At least initially, Mulvey will pitch out of the bullpen, but that could change depending on how Billy Buckner pitches Thursday.
"However I can help the team is fine by me," Mulvey told D-backs manager A.J. Hinch when informed of his role.
Mulvey will not be the only new face in the Arizona bullpen Wednesday night.
The team also recalled Bryan Augenstein from Double-A Mobile. The right-hander is also a candidate to get a start in the final few weeks of the season before he heads to the Arizona Fall League.
"It's always better to have too much pitching than not enough," Hinch said. "He's obviously a good guy to have down in our bullpen, can extend some innings, can start him. Pretty sure [he's] going to pitch in the Arizona Fall League, [this] sort of bridges that gap between the Minor League season and the Fall League."
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.