Former Hawthorn premiership defender Stephen Gilham has also been elevated to the leadership group, joining last year’s leaders Callan Ward, Phil Davis and Tom Scully.
The captains and vice-captains for 2014 will be announced in the new year.
GIANTS Head Coach Leon Cameron said the elevation of Shaw, Mumford and Gilham would add much needed experience to the leadership group and help fast track the club’s young players.
"These three guys are premiership players at the clubs they’ve previously been at but they also offer 10 years of experience in football generally and not only on the field but off the field," said Cameron.
“They will complement our existing leaders Callan Ward, Phil Davis and Tom Scully who will also benefit from their experience and maturity.”
Shaw, 28, played 173 games for Collingwood and was one of its best players in its 2010 premiership side. He joined the club in the recent trade period along with 27 year-old Mumford, who's played 100 AFL games, including the Swans 2012 premiership.
Mumford said he was thrilled to join the leadership group ahead of his first year at the GIANTS.
“It’s something I’m really looking forward to. I'll look to really lift my leadership skills and to be able to share some of the knowledge of my 100 games with the younger guys," said Mumford.
"I think it’s just about pushing these younger guys to get the best out of themselves and that’s something I’m really going to try and do over the next three or four years."
Shaw said he was looking forward to the challenge of taking on a leadership role at his new club.
"It was something I thought about when I first came to the club, being an elder-statesman and having such a youthful group, my experience and the places I've been and the experiences I've had would be a perfect fit for me to go in there," said Shaw.
"I think I'm pretty approachable to the boys, I get along with everyone and obviously this group is so young and needs a bit of guidance coming through so when things get tough I'm going to be the one that stands up."
The GIANTS have also announced eight young players who’ll make up the emerging leaders’ group. They are Stephen Coniglio, Devon Smith, Adam Treloar, Jeremy Cameron, Dylan Shiel, Curtly Hampton, Matt Buntine and Jonathan Giles.
Cameron said these players would work closely with the senior leadership to deliver strong leadership for the GIANTS over the next decade.
“We think this is a great opportunity to develop our young players as leaders on and off the field and benefit from the experience and knowledge they will gain not just from our senior group but also the player development coordinator Simon Katich,” Cameron said.