Jones was elevated to the role on Wednesday in place of Jack Trengove and alongside Jack Grimes who will lead the Demons for a third straight year.
The reigning two-time best-and-fairest winner said he was ready for the huge challenge ahead of him and the increased attention that would come his way.
"It's a great honour. I feel pretty privileged to be in this position probably mainly for the journey that I've had so far at the footy club (because there) hasn't been very much on-field success," Jones said at the MCG on Wednesday.
"To be appointed by the board, and in particular voted by your peers, I feel obviously a great privilege to hold that position and to be in charge of leading the footy club into a successful period.
"I think now we're on the right track, I think in the past I've been through some pretty rough times but I think there's some real light at the end of the tunnel now.
"I think the footy club is really sorting itself out.
"Obviously there's going to be a bit more pressure, there's pressure on myself to step up as a player individually but as a captain I just feel if I can continue to do what I'm doing then I'll be able to lead the way."
Grimes admitted that when he was first handed the co-captaincy in 2012, he 'fell in that trap' of trying to be someone he wasn't and he advised Jones against making the same mistake.
"The first thing I did say to him was just to not change and he's got into the position because of what he was doing already," Grimes said.
While Trengove stepped down from the co-captaincy in November, Grimes was keen to remain in his post because he believed he improved as a leader and that he was better for the extremely tough times he had experienced in being the figurehead of the club during some very bleak times recently.
"I see myself as a much better captain today than what I was day one," Grimes said.
"I feel like although I have been through a fair bit over the last couple of years ... I've learned a lot from it and I really feel I've developed as a person and as a leader as well.
"I made it clear (to coach Paul Roos) that there were times when I struggled but at the same time they were the times when I developed the most as a person too."
Roos said it became increasingly clear as the summer progressed that Jones and Grimes were the standout candidates to captain Melbourne.
"Nathan was held in really high regard by all the players and then we got to learn why as a coaching group because his work ethic is so good, he's hungry to learn (and) as a past two-time best-and-fairest winner it's great to have a player that wants to continue to get better," Roos said.
"Jack, through being captain in the past, was still held in really high regard and then Nathan through his efforts on the field, but more importantly off the field, was seen certainly equal to Jack as one of the real leaders of the club."