The Rays previously received Minor League second baseman Nick Solak from the Yankees and Anthony Banda from Arizona, while the Yankees received Brandon Drury and a Minor League pitcher from the D-backs.
McWilliams, 22, was 1-1 with a 2.10 ERA and 32 strikeouts in five starts for Class A Advanced Visalia. He ranked third in the California League in strikeouts, including a career-high 12 in his last start on Thursday.
McWilliams' velocity is in the upper 90s, according to Rays manager Kevin Cash.
"Big, tall kid, a lot of leverage. I think we're excited about both of them," Cash said.
The 24-year-old Poche hadn't allowed a run in 11 innings of work across nine appearances this season with Double-A Jacksonville.
"We gave up a really good player in Steven Souza, but we do like, between Anthony Banda, Nick Solak, and now these two guys," Cash said. "We feel fortunate we're able to bring all of them into our system and kind of continue to stockpile a pretty good core group that we think we have."
McWilliams will be assigned to Class A Advanced Charlotte, while Poche will join Solak at Double-A Montgomery.
Kyle Beery is a contributor to MLB.com based in Detroit.