Prior to Sunday afternoon's game, the Rays had yet to make an official announcement, but Montgomery's Web site had an official press release on the move.
According to the Biscuits, Price will arrive in Montgomery on Sunday evening and is expected to join the team's roster early this week.
Price could start for the Biscuits as soon as Thursday, during Montgomery's six-game series in Mobile, Ala.
Drafted in June 2007, the 22-year-old signed a contract with the Rays on Aug. 15, 2007, worth up to $11.25 million with $8.5 million guaranteed.
After an impressive Spring Training, Price was delayed in beginning his professional career due to a left elbow strain. But the Vanderbilt alum didn't waste any time establishing himself at Vero Beach.
In his debut on May 22 he threw five shutout innings, allowing two hits and striking out four.
In six starts at Vero Beach, Price went 4-0 with a 1.82 ERA. He struck out 37 batters and walked just seven in 34 2/3 innings.
Brittany Ghiroli is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.