Cashner, 21, the 19th overall pick in the First-Year Player Draft, was expected to come to Chicago this week to undergo a physical, and, if he passes, he could workout at Wrigley Field on Thursday.
As part of the deal, reported Tuesday on Scout.com, Cashner will receive a $1.54 million signing bonus, plus $75,000 that will go toward finishing school. He also will receive an invitation to big league Spring Training camp in 2009.
Vescovo told a Houston television station that Cashner wanted to get the deal done quickly.
"Rather than holding out until Aug. 14 (the day before the deadline for teams to sign their Draft picks), I will be able to get a lot of work in now," Cashner told KRIV-TV in Houston. "I'm really glad to get this done. Now I can start playing baseball. My big moment will come when I put my name on that piece of paper."
Carrie Muskat is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.