The Giants said Jones, a third-round draft pick from LSU, was scheduled to be released from the Hospital for Special Surgery in Manhattan on Tuesday morning to return to home.
Jones' father said earlier this month that his son had thought about playing football again, but his priority is regaining his health.
Jones was transferred to the hospital June 29 after sustaining serious injuries to his left leg and ankle five days earlier in an early morning car accident in New Orleans.
Jones has undergone several surgeries in New Orleans and New York since the accident. He plans to rest and recuperate in New Orleans before returning to New York in several weeks and undergoing more surgery.
The Giants open training camp Sunday at the University at Albany. The team has neither made a roster move with Jones nor discussed how his injuries might affect his career.
Jones signed his contract about one week before the accident.
"Chad is in great spirits and excited to be getting out of the hospital," said Giants vice president of medical services Ronnie Barnes, who visited Jones on Tuesday morning. "All has gone well thus far for Chad, and he will return in probably six to eight weeks for another surgical procedure."
A two-sport star in college, Jones was injured when his SUV slammed into a pole in a dawn wreck.
Police weren't able to test Jones' blood-alcohol level before he went into surgery. Officers were able to interview Jones' two passengers, who had only minor injuries, and found no evidence that alcohol was a factor in the crash.
The hospital likely conducted blood or urine tests on Jones, but authorities haven't decided whether to subpoena those, police said. Jones was cited for careless operation of a vehicle.
A playmaking safety, Jones was part of LSU's 2007 BCS national championship football team and was a left-handed relief pitcher for the 2009 Tigers baseball squad that won the College World Series. He was drafted by Major League Baseball's Milwaukee Brewers two months after the Giants selected him in the NFL draft.
Copyright 2010 by The Associated Press