Jones spent the last two weeks undergoing intense physiotherapy and he was forced to watch from the stands as Wales beat the Pacific Islanders and Canada.
While his ability to kick is still to be tested this week, in every other way Jones insists he is ready to tackle the All Blacks.
The 28-year-old said: "I am very relieved. I have worked intensely with the physio over the last few weeks. It has been a frustrating period but I am glad to be back to full fitness.
"I was doing three or four sessions a day and it's not just the treatment, but the rehabilitation.
"I had a lot of exercises to do but that has improved the knee and over the next few days I will have some kicking sessions with Neil Jenkins."
Wales head coach Gareth Jenkins needed Jones back in action to face the rampant All Blacks, who have already beaten England and France this month.
Jenkins wanted his most experienced and "defiant" axis through the midfield and named Sonny Parker at inside centre, between Jones at fly-half and Tom Shanklin.
"It's huge to have Steve in the team," said Jenkins.
"Steve has come back in fit and enthusiastic. The weeks he has had off have regenerated him.
"It has allowed him to build a focus and Steve has been a huge part of a positive week's training. His captaincy is a big part of the way the team respond."
Jones' return to the fold was also welcomed by his opposite number, All Blacks fly-half Dan Carter.
Carter said: "He is a great player. He has been around for a while and he reads the game well.
"Having him back in the side is a big plus for the Wales team because of his experience and the way he plays the game. He is a good bloke as well so it is good to see him back.
"I was a bit surprised that Gavin Henson wasn't selected (at inside centre). But Sonny Parker played pretty well last weekend.
"Sonny is a strong and powerful player, solid both in defence and attack. We see him as a threat and I am sure Gavin will get a run this weekend."
Jones may be sick of the sight of Carter lining up against him in a black jersey.
In 2004, New Zealand pipped Wales 26-25 at the Millennium Stadium. Last year, Carter inspired the All Blacks to a series victory over the Lions.
They faced each other again 12 months ago, when Carter's 26 points helped New Zealand to a crushing 41-3 victory over a depleted Wales.
Wales have not beaten New Zealand for 53 years, but Jenkins said: "We have been close. Two years ago we won the performance, not the game. Hopefully we can go a step further."