Less than 40 votes separated the club leaders, with McVeigh taking out the coveted award with 807 votes ahead of Jack, who polled 769.
Upon accepting his award for coming in second place, Jack said he was proud to set a positive example for the club in his first year as co-captain alongside McVeigh, who he described as his mentor.
“It was great to see Jarrad win it and to see the two co-captains as the top two is a great sign for the club,” Jack told sydneyswans.com.au.
“Myself and Jarrad, we drive each other and I think we set the standard that we want everyone to get to, and both of us in the top two is a good sign for the club.
“Jarrad’s someone I’ve always looked up to both as a player and as a leader, so it’s an honour to finish in second place alongside him this year.”
McVeigh, who took out his second Bob Skilton Medal, also paid tribute to Jack who produced a stand out season in his first year as co-captain.
“Kieren, the way he’s led this year has been unbelievable,” McVeigh said after accepting his award.
Watch Jarrad McVeigh's acceptance speech in the video player above
“His year last year was great and he’s really stepped up another level this year and I’m really proud of him and the way he’s led the group from the front in his actions and the way he goes about it.
“I’m so proud of him and I’m glad we were both up there, and I’m sure he deserves it just as much as I do.”
Swans coach John Longmire was equally impressed with this year’s Bob Skilton Medal results and said he couldn’t be more proud of what his leaders achieved in 2013.
The coach highlighted McVeigh and Jack’s All-Australian honours as another important acknowledgment for the leaders of his team.
“You couldn’t have asked for any more from your leaders and the leadership group, who have been remarkably resilient this year with the level of consistency they’ve been able to deliver,” Longmire said on Friday night.
“What better example than having your two co-captains come out and have All-Australian years and finish one and two in your best and fairest.
“I couldn’t be more proud with how they’ve been able to lead the club.”
