Radziewski could be joined in Tri-City by college teammate Alex Hernandez, a second baseman from Miami taken in the 40th round, who has also agreed to terms. Hernandez is waiting to find out where he will be sent.
Radziewski, 5-foot-10, 195 pounds, was 8-2 for the Hurricanes this season with an ERA of 2.86. Radziewski struck out 111 batters with 49 walks, and he was named to the Louisville Slugger All-America second team and the Rawlings All-America third team.
Radziewski originally was drafted by the Cardinals in the 29th round in 2013 after going 9-3 with an ERA of 1.78 in 14 starts. Radziewski is from Miami and went to Florida Christian High School.
"Being away from home for the first time, you don't know what to expect," he said. "I'm excited to start my professional career."
MLB.com reported over the weekend that the Astros had agreed with eighth-round pick Bobby Boyd, a center fielder from West Virginia University, and 10th-round pick Jay Gause, a right-handed pitcher from Faulkner University in Alabama.
Sixth-round pick Brock Dykxhoorn, a right-handed pitcher from Central Arizona College, said on Saturday that he had agreed to a signing bonus and was sorting out the final details of the contract.
No. 1 overall pick Brady Aiken, a left-handed pitcher from the San Diego area, has agreed to a $6.5 million signing bonus and could have a contract done this week.
Brian McTaggart is a reporter for MLB.com and writes an MLBlog, Tag's Lines. Follow @brianmctaggart on Twitter. Adam Lichtenstein is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.