Mumford started his career as a rookie at Geelong, where he played 21 games but missed selection in the 2009 premiership.
He then moved to the Swans after accepting a three-year, million-dollar offer from the club to move north. He was a very good player for the club, playing 79 games and being first ruck in the club's 2012 premiership, when he performed well despite entering the game under an injury cloud.
He was also runner-up in the club's best and fairest in 2010.
Despite his success at the Swans, Mumford accepted the GIANTS' offer, which was impossible for the Swans to match once Lance Franklin agreed to join the club via free agency.
He is the first player the GIANTS have officially secured during the Gillette Trade Period.
The Giants now have picks No.1, 2, 19 and 20 after trading Dom Tyson for picks No.2, 20 and 72 on Friday morning. Melbourne received picks No.9, 53 and Tyson.