Purke was the 14th overall pick in June.
"It's disappointing," Rangers general manager Jon Daniels said after Monday night's deadline passed. "You draft a player with every intention of signing him. But we couldn't make it work. There's a silver lining that we get the pick back next year, but I would have preferred having him in a Ranger uniform."
The 18-year-old Purke pitched for Klein High School outside Houston, going 4-2 with a 1.18 ERA as a senior. He struck out 91 and walked only seven in 47 1-3 innings, featuring a 95 mph fastball.
Purke passed a Rangers' physical last weekend. On Saturday night he met with team president Nolan Ryan and his family watched the Rangers play the Boston Red Sox from a private suite at Rangers Ballpark.
In case he was unable to sign, Purke had committed to TCU in Fort Worth. Now it appears he will pitch for the Horned Frogs.
The Rangers will continue talks with representatives for another high pick, right-hander Tanner Scheppers from Fresno State. Scheppers, the 44th overall selection taken in the supplemental first round, has been pitching for St. Paul in the independent American Association.
Scheppers wasn't subject to Monday night's deadline, so the Rangers can continue to negotiate with him until the 2010 draft.