Jones said Claiborne was the second best player on the Cowboys’ draft board behind quarterback Andrew Luck and the highest-rated cornerback by the team since Deion Sanders.
The Cowboys traded the 14th pick and the 45th overall (second round) to move up to select Claiborne.
"He is the best cornerback prospect our scouts have graded since Deion," Jones said. "He is a difference maker."
Claiborne underwent surgery last month repair a torn ligament in his left wrist. He will be ready to go for training camp but will miss organized team activities and the minicamp in June.
Claiborne said he will be ready for training camp.
"They sacrificed a lot to come down to get me, but I feel like I'm worth it," Claiborne said. "I know my talents. I know what kind of guy they're looking for. They want me to come in and play right away and be a lock down guy, and I feel like in the right hands, which I am, I feel like I can come in right away and do that."
Jones said Claiborne is the continuation of a long process of trying to improve a horrid secondary and Cowboys pass defense which gave up more passing yards the past two seasons than any time in team history. The Cowboys signed Brandon Carr to a five-year, $50.1 million contract in the offseason and now have added best defensive player in the draft.
"We've been needing to work on the secondary," Jones said. "When Wade (Phillips) was (coach), I talked to Wade about it. This is not something that's new. We had hoped upon hope and certainly (defensive coordinator) Rob (Ryan) had hoped with the head of the pack that Terence (Newman) could really be what we wanted him to be. So obviously that didn't work out. That's just the way it is. But I like the way we've come back."
The Cowboys now have a crowded secondary with Carr, Claiborne, former starter Mike Jenkins, a 2008 first-round pick and former Pro Bowler, to go along with nickel back Orlando Scandrick.
Coach Jason Garrett said all will play, although the Cowboys could move Jenkins before the season. He said Claiborne is a difference maker worth the gamble.
"Cornerback is a premium position," Garrett said. "We feel to add a guy like this was the right thing to do. He has instincts. He has vision. He has the ability to make plays. He is a game-changing playmaker. He can make plays on the ball and change the game. He is also an outstanding kickoff returner. That is certainly another part of why he is an attractive player."
Claiborne is the team's highest pick since they took Newman fifth overall in 2003.
It was Jones' 59th draft-day trade since 1989, the 18th involving a first-round pick.
Claiborne, 5-foot-11, 188 pounds, was first-team All-American in 2011 and won the Jim Thorpe Award as the nation's best defensive back. He had 11 interceptions the past two years, including six in 2011. He is also a standout kickoff returner.
"We said before the draft the only player we had an interest in moving up to get was Claiborne," Jones said. "We had serious doubts he would get to six. But then the opportunity presented itself and they started taking players in front of him and the price was right for us. To go from 14 to six, you got give up something. By a lot of charts you got to give up more. To a get a difference maker on defense, we pulled the trigger."