The Phillies optioned left-hander Elvis Araujo (1-1, 5.87 ERA in 27 appearances) to Triple-A Lehigh Valley to make room for Velasquez on the 25-man roster.
It moves Morgan (1-6, 6.55 ERA) into a relief role for the first time in his career.
"We're going to get a look at him in that role for the time being, which doesn't mean he's never going to start again for us," Phillies manager Pete Mackanin said. "But at this point we want to give it a look to see if he can pitch out of the bullpen."
The Phillies think Morgan's combination of pitches and stuff might play better in the bullpen.
"It's an awesome opportunity," Morgan said. "I need to take advantage of it. I've never done it before, but I will give it a shot. I'm excited."
Todd Zolecki has covered the Phillies since 2003, and for MLB.com since 2009. Read his Phillies blog The Zo Zone, follow him on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.