The extension apparently aimed to mitigate the cancellation of Duke's 2006 season amid rape allegations against three squad members. Those charges were later dropped.
"These individuals were involved in an unusual circumstance that we believe warrants providing them the opportunity to complete their four years of competition," said NCAA spokesman Jennifer Strawley.
The NCAA extended an additional year of competition for those players who had remaining eligibility after the 2006 season was canceled.
The NCAA considered several factors, including the unusual and extenuating circumstances surrounding the cancellation, the hardship endured by the team from the false allegations, and the unanimous endorsement by conference university presidents for the waiver.
The announcement came two days after Duke lost to Johns Hopkins in the championship game of the NCAA Tournament.