The 27-year-old big man, who played in the Swans' 2012 flag and has racked up 100 AFL games, will be traded to the Giants.
Less than 24 hours after the Lance Franklin bombshell that saw the two-time Hawthorn premiership star turn his back on a weighty deal from GWS, the Giants have finally broken through and landed an established big name.
The Giants wasted no time getting the ruckman into the orange and charcoal, posting a photo of him on their website with the distinctive jumper on Wednesday.
The Giants must still facilitate a trade for the out-of-contract player or use their first selection in the NAB AFL Pre-season Draft to secure him.
But Mumford, the former Cat, has expressed his enthusiasm about joining the Swans' crosstown rivals on a three-year deal.
"The Giants are an exciting club with a great future and I couldn't be happier to be moving across Sydney to join them," Mumford said.
"They have a talented young midfield and it's a great opportunity to help them go to the next level and achieve on-field success."
Mumford's manager Anthony McConville said his client had considered moving home to Victoria, but the decision to join the Giants was one protecting his future in the game.
"That was always in the back of Shane's mind is to whether he stayed in Sydney or moved back down to Melbourne," McConville said.
"At the end of the day it was up to Shane to make a decision and he was really happy and excited about staying in Sydney and joining the GWS Giants.
"It was really about protecting Shane's career going forward."
McConville said Tuesday's news that Hawthorn superstar Lance Franklin had accepted an offer from the Sydney Swans meant Mumford's future at the club appeared untenable.
While not wanting to go into specifics, he admitted Mumford had accepted a healthy financial deal from the Giants.
"That sort of highlighted to us particularly there probably wasn't going to be the room to fit Shane into the equation," he said.
"Further discussions were held and…it was a good outcome [financially], put it that way."
Coach Leon Cameron said the acquisition was a "great coup" for the fledgling club.
"This shows that high-calibre players are prepared to join our club in Western Sydney and Canberra, and we are delighted that Shane has agreed to join us," Cameron said.
"We said we needed to target an experienced ruckman and with the addition of Shane we have landed a quality player.
"As our No.1 ruckman he will take some of the pressure off Jonathan Giles while we continue to develop Andrew Phillips and Tom Downie, and gives us depth in our ruck stocks.
"We have every confidence in our list management strategy and will continue to be aggressive in the trade period to acquire the experienced players we need at the Giants."
Twitter: @AFL_JenPhelan
