Morris has gone 4-0 with a 3.80 earned run average over 21 games with the Pirates this season.
In 81 career games, all with the Pirates, the 27-year-old right-hander has posted a 9-7 record with a 3.46 ERA.
Pirates' GM Neal Huntington got a stronger Draft presence with the deal. The acquired pick becomes the team's second-highest overall; the Pirates' regular first-round choice, at No. 24, originally was not going to be repeated until No. 64.
"We feel this trade will have a positive impact on our organization in the short, moderate and long term," said Huntington. "In the short term, this trade will add a quality prospect to our system that will enhance our ability to make additional prospect-for-Major League-player-type deals while helping us to better sustain crucial prospect depth.
"Additionally, we feel we have made this move from a position of strength, as we have kept our core bullpen intact. In the moderate and long term, we add an additional first-round talent that we project to play a significant role on future Pirates teams."
Morris' spot on the 25-man roster was filled by Casey Sadler, who was recalled from Triple-A Indianapolis, where he'd been 6-1 in eight starts with a 2.66 ERA.