Carlton Dotson, 21, made the decision along with his lawyers, attorney Sherwood Wescott said.
"We're not giving any real reasons why we didn't (file an appeal)," Wescott said. "It was a collaborative effort. Everyone, including our client, came to a decision this was the route we wanted to take."
Texas authorities have about three weeks to transport Dotson. Details of the transfer most likely won't be released for security reasons, Wescott said.
Dotson's attorneys have been opposing his extradition to McLennan County, Texas, since Dotson was arrested in July and charged with the shooting death of Patrick Dennehy, 21. He has been held at a Kent County jail in Chestertown, 55 miles from his hometown of Hurlock on Maryland's Eastern Shore.
The former Baylor player has appeared in court three times as officials shuffled extradition paperwork between Texas and Maryland. Last month, Maryland Gov. Robert Ehrlich signed a warrant agreeing to turn Dotson over to prosecutors in Texas.
A Kent County District Judge served Dotson with the governor's warrant in court last week and Dotson's attorneys had faced a Friday deadline to file their next appeal.
Filing the appeal would have further delayed extradition, but officials in both states have said chances were slim that Dotson would have been successful.
In Texas, Dotson will face another arraignment and bail review hearing before trial, Wescott said.
Dotson was arrested July 21 after calling police from a supermarket, saying he was hearing voices and needed counseling. Officers took him to a hospital, where he contacted the FBI.
Dennehy's body was found on July 25 in a field southeast of Waco, Texas. An autopsy determined he died of two gunshot wounds to the head.
The case has rocked the Baptist school and its basketball program. Coach Dave Bliss and the university's athletic director resigned Aug. 8. School investigators said they discovered that two players were receiving improper financial aid and staff members did not properly report failed drug tests.